Search results for: logistics equation

Authors: Y. Pala, M. O. Ertas

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In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

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Authors: Giulio Mangano, Alberto De Marco, Giovanni Zenezini

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The concept of City Logistics (CL) has emerged to improve the impacts of last mile freight distribution in urban areas. In this paper, a System Dynamics (SD) model exploring the dynamics of the diffusion of a ICT platform for CL management across different populations is proposed. For the development of the model two sources have been used. On the one hand, the major diffusion variables and feedback loops are derived from a literature review of existing diffusion models. On the other hand, the parameters are represented by the value propositions delivered by the platform as a response to some of the users’ needs. To extract the most important value propositions the Business Model Canvas approach has been used. Such approach in fact focuses on understanding how a company can create value for her target customers. These variables and parameters are thus translated into a SD diffusion model with three different populations namely municipalities, logistics service providers, and own account carriers. Results show that, the three populations under analysis fully adopt the platform within the simulation time frame, highlighting a strong demand by different stakeholders for CL projects aiming at carrying out more efficient urban logistics operations.

Keywords: city logistics, simulation, system dynamics, business model

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Authors: S. N. S. Thein, H. L. Yang, Z. B. Liu

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There are many modes of transport. Among them, maritime transport is a major transportation mode of international trade. In the Republic of the Union of Myanmar (Burma), water transportation served as one of the most important modes of transport for country's exports and imports. Getting the accurate information and data-gathering activity are the most important aspects for any study field. Therefore, in this research, a historical review of the development of ports in Myanmar and how they have changed had been carried out. All the relevant literature and documents have also been reviewed, studied, and organized. The sources of collected data are from reports, journals, internet, as well as from the publications of authorized organizations and international associations. To get better understanding about real situation of maritime transport and logistics in Myanmar; current condition of existing ports, expansion and on-going projects, and future port development plans are described successively. Hence, the main purpose of this study is to build up a comprehensive picture of maritime transport and logistics, in addition to border trade within ASEAN and Myanmar. It will help for academic researchers, decision makers, and stakeholders for national planning as well as for the local and foreign investors to recognize current situation of maritime transport and logistics in Myanmar.

Keywords: ASEAN, border trade, logistics, maritime transport, ports of Myanmar

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Authors: Sharon-Yasotha Veerayah-Mcgregor, Valipuram Manoranjan

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A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient.

Keywords: inverse/backward equation, operator-splitting, Nagumo equation, ill-posed, finite-difference

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Authors: T. Spiegel, J. Siegmann, C. F. Durach

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Challenges resulting from an international and dynamic business environment are increasingly being passed on from manufacturing companies to external service providers. Especially providers of complex, customer-specific industry services have to cope with continuously changing requirements. This is particularly true for contract logistics service providers. They are forced to develop efficient and highly flexible structures and strategies to meet their customer’s needs. One core element they have to focus on is the reorganization of their service development and sales process. Based on an action research approach, this study develops and tests a concept to streamline tender management for contract logistics service providers. The concept of modularized service architecture is deployed in order to derive a practice-oriented approach for the modularization of complex service portfolios and the design of customized quotes. These findings are evaluated regarding their applicability in other service sectors and practical recommendations are given.

Keywords: contract logistics, modularization, service development, tender management

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Authors: Tuğçe Yavaş Akış

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In recent years, due to an increased use of radioactive materials, radioactive sources are constantly being transported via air, road and ocean ways for medical, industrial, research etc. purposes throughout the world. The quantity of radioactive materials transported all around the world varies from negligible quantities in shipments of consumer products to very large quantities in shipments of irradiated nuclear fuel. Radioactive materials have been less attractive for social science researchers in literature. In this study, it is aimed to discover desired flow of radioactive materials from logistics service quality (LSQ) perspective. In doing so, case study approach will be employed by using secondary data collected from one of the world’s leading transportation companies’ customer care system reports. Movement of radioactive cargoes containing IR-192 and logistics process will be analyzed with the help of logistics service quality dimensions. Based on the case study that will be conducted, interaction between dimensions, the importance of each dimension in desired flow, and their relevance with desired flow of radioactive materials will be explained. This study will bring out the desired flow of radioactive materials transportation and be a guide for all other companies, employees and researchers.

Keywords: logistics service quality, LSQ dimension , radioactive material, transportation

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Yuan Yan Tang, Lina Yang, Hong Li

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Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments.

Keywords: harmonic model, partial differential equation (PDE), integral equation, integral representation, boundary measure formula, wavelet collocation

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Authors: Alhasan Hakami, Arun Kumar, Sung J. Shim, Yousef Abu Nahleh

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In recent years, many high intensity earthquakes have occurred around the world, such as the 2011 earthquake in Tohoku, Japan. These large-scale disasters caused huge casualties and losses. In addition, inefficient disaster response operations also caused the second wave of casualties and losses, and expanded the damage. Effective disaster management can be used to respond to the chaotic situation, and reduce the damage. However, some inefficient disaster response operations are still used. Therefore, this case study chose the 921 earthquakes for analysing disaster emergency logistics problems and proposed the Soft Systems Methodology (SSM) to solve disaster emergency logistics problems. Moreover, it analyses the effect of human factors on system operation, and suggests a solution to improve the system.

Keywords: soft systems methodology, emergency logistics, earthquakes, Japan, system operation

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Authors: Colette Malyack, Pius Egbelu

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Business-to-Customer (B2C) delivery options have improved to meet increased demand in recent years. The change in end users has forced logistics networks to focus on customer service and sentiment that would have previously been the priority of the company or organization of origin. This has led to increased pressure on logistics companies to extend traditional B2B networks into a B2C solution while accommodating additional costs, roadblocks, and customer sentiment; the result has been the creation of the omnichannel delivery network encompassing a number of traditional and modern methods of package delivery. In this paper the many solutions within the omnichannel delivery network are defined and discussed. It can be seen through this analysis that the omnichannel delivery network can be applied to reduce the complexity of package delivery and provide customers with more options. Applied correctly the result is a reduction in cost to the logistics company over time, even with an initial increase in cost to obtain the technology.

Keywords: network planning, last mile delivery, omnichannel delivery network, omnichannel logistics

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Authors: N. Jena, Nitin Seth

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Globalization and free trade has forced the organizations to continuously rethink and rework on the increasing cost of logistics. World wide, it is visualized that on one side the steel sector is witnessing rapid growth and on the other side it is facing huge challenges in terms of availability of raw materials for uninterrupted production. Inbound logistics also gains significant importance for ensuring the timely availability of raw materials. It is seen that in Indian steel sector logistic cost is still very large and challenging. Effectively managing the inbound logistics in steel decides the profitability and serviceability of the organization. Effective management of inbound logistics also has a major role on the inventory of the organization. Since, the logistics for the steel industry in India is evolving rapidly and it is the interplay of infrastructure, technology and new types of service providers that will define whether the industry is able to help its customers to reduce their logistics costs. Integration of Logistics has been treated as one of the most potential area for the companies to provide a base for cost reduction. In spite of the proven area for benefits for the industry, it is very surprising that none of the researchers have explored this area. Although, many researchers explored the subject of logistics in steel industry, but their perspective varied from exploring and understanding the associated cost and finding out the relations between them. Visualizing a potential gap, the present research is under taken to explore the integration opportunities in inbound logistics for steel sector. Typically in Indian steel sector where in most of the manufacturers depend on imported materials for processing the logistics is very challenging and accounts for transactions at supplier – who is situated in different country, shipper- who is transporting the material to the host country, regulators in both countries-that include customs and various clearing agents, local logistics service providers and local transporters/handlers. It is seen that In bound logistics cost in the steel sector is very high and accounts for about 15-16% of the turn over, integration of information across different channels provides and opportunity for improvements and growth of the organization. In the present paper, a case of leading steel manufacturer has been taken and the potentials for integration of information across various partners have been identified. The paper provides the identification of grey area in steel sector for major improvements in cycle time and lowering the inventories by integration of information. Finally, based on integration of information, the paper presents a business information framework for steel sector.

Keywords: integration, steel sectors, suppliers, shippers, customs and cargo agents, transporters

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Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis

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Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation.

Keywords: Hodgkin-Huxley equation, solitary solution, existence condition, operator method

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Authors: Nara Guimarães, Marcelo Aquino Martorano, Douglas Gouvêa

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An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles.

Keywords: Cahn-Hilliard equation, miscibility gap, phase separation, dimensional domains

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Authors: Hesamoddin Abdollahpour, Roghayeh Abdollahpour, Elham Rahgozar

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This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task.

Keywords: large amplitude, free vibrations, analytical solution, Danell Equation, diagram of phase plane

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Authors: Yousef Abu Nahleh, Arun Kumar, Fugen Daver, Reham Al-Hindawi

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Despite the availability of natural disaster related time series data for last 110 years, there is no forecasting tool available to humanitarian relief organizations to determine forecasts for emergency logistics planning. This study develops a forecasting tool based on identifying probability of disaster for each country in the world by using decision tree modeling. Further, the determination of aggregate forecasts leads to efficient pre-disaster planning. Based on the research findings, the relief agencies can optimize the various resources allocation in emergency logistics planning.

Keywords: decision tree modeling, forecasting, humanitarian relief, emergency supply chain

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Authors: Armen Grigoryan, Milena Arakelyan

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The idea of smart logistics is still quite a complicated one. It can be used to market products to a large number of customers or to acquire raw materials of the highest quality at the lowest cost in geographically dispersed areas. The use of smart contracts in logistics and supply chain management has the potential to revolutionize the way that goods are tracked, transported, and managed. Smart contracts are simply computer programs written in one of the blockchain programming languages (Solidity, Rust, Vyper), which are capable of self-execution once the predetermined conditions are met. They can be used to automate and streamline many of the traditional manual processes that are currently used in logistics and supply chain management, including the tracking and movement of goods, the management of inventory, and the facilitation of payments and settlements between different parties in the supply chain. Currently, logistics is a core area for companies which is concerned with transporting products between parties. Still, the problem of this sector is that its scale may lead to detainments and defaults in the delivery of goods, as well as other issues. Moreover, large distributors require a large number of workers to meet all the needs of their stores. All this may contribute to big detainments in order processing and increases the potentiality of losing orders. In an attempt to break this problem, companies have automated all their procedures, contributing to a significant augmentation in the number of businesses and distributors in the logistics sector. Hence, blockchain technology and smart contracted legal agreements seem to be suitable concepts to redesign and optimize collaborative business processes and supply chains. The main purpose of this paper is to examine the scope of blockchain technology and smart contracts in the field of logistics and supply chain management. This study discusses the research question of how and to which extent smart contracts and blockchain technology can facilitate and improve the implementation of collaborative business structures for sustainable entrepreneurial activities in smart supply chains. The intention is to provide a comprehensive overview of the existing research on the use of smart contracts in logistics and supply chain management and to identify any gaps or limitations in the current knowledge on this topic. This review aims to provide a summary and evaluation of the key findings and themes that emerge from the research, as well as to suggest potential directions for future research on the use of smart contracts in logistics and supply chain management.

Keywords: smart contracts, smart logistics, smart supply chain management, blockchain and smart contracts in logistics, smart contracts for controlling supply chain management

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Authors: Giuseppe Timperio, Robert de Souza

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Logistics operations in the context of disaster response are characterized by a high degree of complexity due to the combined effect of a large number of stakeholders involved, time pressure, uncertainties at various levels, massive deployment of goods and personnel, and gigantic financial flow to be managed. It also involves several autonomous parties such as government agencies, militaries, NGOs, UN agencies, private sector to name few, to have a highly collaborative approach especially in the critical phase of the immediate response. This is particularly true in the context of L3 emergencies that are the most severe, large-scale humanitarian crises. Decision-making processes in disaster management are thus extremely difficult due to the presence of multiple decision-makers involved, and the complexity of the tasks being tackled. Hence, in this paper, we look at applying ICT based solutions to enable a speedy and effective decision making in the golden window of humanitarian operations. A high-level view of ICT based solutions in the context of logistics operations for humanitarian response in Southeast Asia is presented, and their viability in a real-life case about logistics network design is explored.

Keywords: decision support, disaster preparedness, humanitarian logistics, network design

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Authors: S. Mousavian, F. Mousavian, V. Nikkhah Rashidabad

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Cubic equations of state like Redlich–Kwong (RK) EOS have been proved to be very reliable tools in the prediction of phase behavior. Despite their good performance in compositional calculations, they usually suffer from weaknesses in the predictions of saturated liquid density. In this research, RK equation was modified. The result of this study shows that modified equation has good agreement with experimental data.

Keywords: equation of state, modification, ammonia, genetic algorithm

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Authors: Muna Alghabshi, Edmana Krishnan

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A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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Authors: Benedict Barnes, Anthony Y. Aidoo

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A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard.

Keywords: divergence regularization method, Helmholtz equation, ill-posed inhomogeneous Cauchy boundary conditions

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Authors: Arun Kumar, Neelesh Haulder

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This paper identifies and resolves some key issues relating to a specific aspect within the supply chain logistics of the public health care industry in the Republic of Mauritius. The analysis and the proposed solution are performed using soft systems methodology (SSM). Through the application of this relevant systematic approach at problem solving, the aim is to obtain an in-depth analysis of the problem, incorporating every possible world view of the problem and consequently to obtain a well explored solution aimed at implementing relevant changes within the current supply chain logistics of the health care industry, with the purpose of tackling the key identified issues.

Keywords: soft systems methodology, CATWOE, healthcare, logistics

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Authors: Mario Winkelhaus, Franz Vallée

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Many companies see horizontal cooperation as a promising possibility to increase their efficiency in outbound logistics. The selection of suitable partners has particular importance in the formation of horizontal cooperation. Up until now, literature mainly focused on general applicable methods for the identification of cooperation partners without a closer examination of the specific area where the cooperation takes place. Thus, specific criteria as a basis for the partner selection in the field of logistics cooperation are missing. To close this scientific gap, an explorative research approach is used to answer the open question of the article. To collect the needed criteria, a qualitative experiment with 20 participants from 16 companies was done. Within this workshop, general criteria, as well as sector-specific requirements, have been identified which were integrated in a partner selection model.

Keywords: horizontal cooperation, logistics cooperation partnering criteria, partner selection

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Authors: Ibrahim Halil Korkmaz, Eren Özceylan, Cihan Çetinkaya

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Logistics function has great potential for increasing sustainable competitive advantage, profitability, productivity, customer satisfaction and decreasing costs in all sectors. The performance of logistics sector, which has such great influence on the overall performance of the economy, attracts more attention of both researchers and sector representatives day by day. The purpose of this study is to determine the effects of research and development expenditures which spent by enterprises operating in the transportation and storage sectors on Turkey’s logistic performance index (LPI). To do so, research and development investment expenditure among the years 2009-2015 of Turkish transportation and storage firms data from the Turkish Statistical Institute and Turkeys country points in the World Bank logistics performance index in the same years data were examined. As the result of the parametric evaluation, it is seen that the research and development expenditures made have a positive effect on the logistic performance of Turkey.

Keywords: logistics performance index, R&D investments, transportation, storage, Turkey

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Authors: Eduarda Dutra De Souza, Gabriela Hammes, Marina Bouzon, Carlos M. Taboada Rodriguez

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The search for minimizing harmful impacts on the environment has become the focus of global society, affecting mainly how to manage organizations. Thus, companies have sought to transform their activities into environmentally friendly initiatives by applying green practices throughout their supply chains. In the logistics domain, the implementation of environmentally sound practices is still in its infancy in emerging countries such as Brazil. Given the need to reduce these environmental damages, this study aims to evaluate the performance of green logistics (GL) in the plastics industry sector in order to help to improve environmental performance within organizations and reduce the impact caused by their activities. The performance tool was based on theoretical research and the use of experts in the field. The Analytic Hierarchy Process (AHP) was used to prioritize green practices and assign weight to the indicators contained in the proposed tool. The tool also allows the co-production of a single indicator. The developed tool was applied in an industry of the plastic packaging sector. However, this tool may be applied in different industry sectors, and it is adaptable to different sizes of companies. Besides the contributions to the literature, this work also presents future paths of research in the field of green logistics.

Keywords: AHP, green logistics, green supply chain, performance evaluation

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Authors: Safa Gharbi, Hayfa Zgaya, Nesrine Zoghlami, Slim Hammadi, Cyril De Barbarin, Laurent Vinatier, Christiane Coupier

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Increasing productivity and quality of service, improving the working comfort and ensuring the efficiency of all processes are important challenges for every warehouse. The order picking is recognized to be the most important and costly activity of all the process in warehouses. This paper presents a new approach using Augmented Reality (AR) in the field of logistics. It aims to create a Head-Up Display (HUD) interface with a Warehouse Management System (WMS), using AR glasses. Integrating AR technology allows the optimization of order picking by reducing time of picking process, increasing the efficiency and delivering quickly. The picker will be able to access immediately to all the information needed for his tasks. All the information is displayed when needed in the field of vision (FOV) of the operator, without any action requested from him. These research works are part of the industrial project RASL (Réalité Augmentée au Service de la Logistique) which gathers two major partners: the LAGIS (Laboratory of Automatics, Computer Engineering and Signal Processing in Lille-France) and Genrix Group, European leader in warehouses logistics, who provided his software for implementation, and his logistics expertise.

Keywords: Augmented Reality (AR), logistics and optimization, Warehouse Management System (WMS), Head-Up Display (HUD)

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Authors: F. U. Rahman, R. Q. Zhang

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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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Authors: Praveen Kumar, R. Uma, R. P. Sharma

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This study investigates the generation of turbulence in a deep-fluid environment using a damped 1D-modified nonlinear Schrödinger equation model. The well-known damped modified nonlinear Schrödinger equation (d-MNLS) is solved using numerical methods. Artificial damping is added to the MNLS equation, and turbulence generation is investigated through a numerical simulation. The numerical simulation employs a finite difference method for temporal evolution and a pseudo-spectral approach to characterize spatial patterns. The results reveal a recurring periodic pattern in both space and time when the nonlinear Schrödinger equation is considered. Additionally, the study shows that the modified nonlinear Schrödinger equation disrupts the localization of structure and the recurrence of the Fermi-Pasta-Ulam (FPU) phenomenon. The energy spectrum exhibits a power-law behavior, closely following Kolmogorov's spectra steeper than k⁻⁵/³ in the inertial sub-range.

Keywords: water waves, modulation instability, hydrodynamics, nonlinear Schrödinger's equation

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Authors: Meruyert Zhassybayeva, Kuralay Yesmukhanova, Ratbay Myrzakulov

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Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found.

Keywords: Fokas-Lenells equation, integrability, soliton, the Hirota bilinear method

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Authors: Ognjen Vukovic

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Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research.

Keywords: Brownian motion, Chern-Simons theory, financial time series, econophysics

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