Search results for: (2+1)-dimensional breaking soliton equation
1146 Some Exact Solutions of the (2+1)-Dimensional Breaking Soliton Equation using the Three-wave Method
Authors: Mohammad Taghi Darvishi, Mohammad Najafi
This paper considers the (2+1)-dimensional breaking soliton equation in its bilinear form. Some exact solutions to this equation are explicitly derived by the idea of three-wave solution method with the assistance of Maple. We can see that the new idea is very simple and straightforward.
Keywords: Soliton solution, computerized symbolic computation, painleve analysis, (2+1)-dimensional breaking soliton equation, Hirota's bilinear form.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1772
1145 New Exact Solutions for the (3+1)-Dimensional Breaking Soliton Equation
Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi
In this work, we obtain some analytic solutions for the (3+1)-dimensional breaking soliton after obtaining its Hirota-s bilinear form. Our calculations show that, three-wave method is very easy and straightforward to solve nonlinear partial differential equations.
Keywords: (3+1)-dimensional breaking soliton equation, Hirota'sbilinear form.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1542
1144 Traveling Wave Solutions for the (3+1)-Dimensional Breaking Soliton Equation by (G'/G)- Expansion Method and Modified F-Expansion Method
Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi
In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.
Keywords: Exact solution, The (3+1)-dimensional breaking soliton equation, ( G G )-expansion method, Riccati equation, Modified Fexpansion method.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2588
1143 Extend Three-wave Method for the (3+1)-Dimensional Soliton Equation
Authors: Somayeh Arbabi Mohammad-Abadi, Maliheh Najafi
In this paper, we study (3+1)-dimensional Soliton equation. We employ the Hirota-s bilinear method to obtain the bilinear form of (3+1)-dimensional Soliton equation. Then by the idea of extended three-wave method, some exact soliton solutions including breather type solutions are presented.
Keywords: Three-wave method, (3+1)-dimensional Soliton equation, Hirota's bilinear form.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1441
1142 Instability of Soliton Solutions to the Schamel-nonlinear Schrödinger Equation
Authors: Sarun Phibanchon, Michael A. Allen
A variational method is used to obtain the growth rate of a transverse long-wavelength perturbation applied to the soliton solution of a nonlinear Schr┬¿odinger equation with a three-half order potential. We demonstrate numerically that this unstable perturbed soliton will eventually transform into a cylindrical soliton.
Keywords: Soliton, instability, variational method, spectral method.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3529
1141 Multiple Soliton Solutions of (2+1)-dimensional Potential Kadomtsev-Petviashvili Equation
Authors: Mohammad Najafi, Ali Jamshidi
We employ the idea of Hirota-s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.
Keywords: Hirota bilinear method, potential Kadomtsev-Petviashvili equation, multiple soliton solutions, multiple singular soliton solutions.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1261
1140 Exact Pfaffian and N-Soliton Solutions to a (3+1)-Dimensional Generalized Integrable Nonlinear Partial Differential Equations
Authors: Magdy G. Asaad
Abstract:The objective of this paper is to use the Pfaffian technique to construct different classes of exact Pfaffian solutions and N-soliton solutions to some of the generalized integrable nonlinear partial differential equations in (3+1) dimensions. In this paper, I will show that the Pfaffian solutions to the nonlinear PDEs are nothing but Pfaffian identities. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions.
Keywords: Bilinear operator, G-BKP equation, Integrable nonlinear PDEs, Jimbo-Miwa equation, Ma-Fan equation, N-soliton solutions, Pfaffian solutions.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1947
1139 Optical Switching Based On Bragg Solitons in A Nonuniform Fiber Bragg Grating
Authors: Abdulatif Abdusalam, Mohamed Shaban
In this paper, we consider the nonlinear pulse propagation through a nonuniform birefringent fiber Bragg grating (FBG) whose index modulation depth varies along the propagation direction. Here, the pulse propagation is governed by the nonlinear birefringent coupled mode (NLBCM) equations. To form the Bragg soliton outside the photonic bandgap (PBG), the NLBCM equations are reduced to the well known NLS type equation by multiple scale analysis. As we consider the pulse propagation in a nonuniform FBG, the pulse propagation outside the PBG is governed by inhomogeneous NLS (INLS) rather than NLS. We then discuss the formation of soliton in the FBG known as Bragg soliton whose central frequency lies outside but close to the PBG of the grating structure. Further, we discuss Bragg soliton compression due to a delicate balance between the SPM and the varying grating induced dispersion. In addition, Bragg soliton collision, Bragg soliton switching and possible logic gates have also been discussed.
Keywords: Bragg grating, Nonuniform fiber, Nonlinear pulse.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1782
1138 Soliton Interaction in Multi-Core Optical Fiber: Application to WDM System
Authors: S. Arun Prakash, V. Malathi, M. S. Mani Rajan
Abstract:The analytical bright two soliton solution of the 3- coupled nonlinear Schrödinger equations with variable coefficients in birefringent optical fiber is obtained by Darboux transformation method. To the design of ultra-speed optical devices, Soliton interaction and control in birefringence fiber is investigated. Lax pair is constructed for N coupled NLS system through AKNS method. Using two-soliton solution, we demonstrate different interaction behaviors of solitons in birefringent fiber depending on the choice of control parameters. Our results shows that interactions of optical solitons have some specific applications such as construction of logic gates, optical computing, soliton switching, and soliton amplification in wavelength division multiplexing (WDM) system.
Keywords: Optical soliton, soliton interaction, soliton switching, WDM.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1859
1137 Characteristic Study on Conventional and Soliton Based Transmission System
Authors: Bhupeshwaran Mani, S. Radha, A. Jawahar, A. Sivasubramanian
Abstract:Here, we study the characteristic feature of conventional (ON-OFF keying) and soliton based transmission system. We consider 20Gbps transmission system implemented with Conventional Single Mode Fiber (C-SMF) to examine the role of Gaussian pulse which is the characteristic of conventional propagation and Hyperbolic-secant pulse which is the characteristic of soliton propagation in it. We note the influence of these pulses with respect to different dispersion lengths and soliton period in conventional and soliton system respectively and evaluate the system performance in terms of Quality factor. From the analysis, we could prove that the soliton pulse has the consistent performance even for long distance without dispersion compensation than the conventional system as it is robust to dispersion. For the length of transmission of 200Km, soliton system yielded Q of 33.958 while the conventional system totally exhausted with Q=0.
Keywords: Soliton, dispersion length, Soliton period, Return-tozero (RZ), Q-factor.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1515
1136 The Direct Ansaz Method for Finding Exact Multi-Wave Solutions to the (2+1)-Dimensional Extension of the Korteweg de-Vries Equation
Authors: Chuanjian Wang, Changfu Liu, Zhengde Dai
In this paper, the direct AnsAz method is used for constructing the multi-wave solutions to the (2+1)-dimensional extension of the Korteweg de-Vries (shortly EKdV) equation. A new breather type of three-wave solutions including periodic breather type soliton solution, breather type of two-solitary solution are obtained. Some cases with specific values of the involved parameters are plotted for each of the three-wave solutions. Mechanical features of resonance interaction among the multi-wave are discussed. These results enrich the variety of the dynamics of higher-dimensional nonlinear wave field.
Keywords: EKdV equation, Breather, Soliton, Bilinear form, The direct AnsAz method.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1455
1135 Realization of Soliton Phase Characteristics in 10 Gbps, Single Channel, Uncompensated Telecommunication System
Authors: A. Jawahar
Abstract:In this paper, the dependence of soliton pulses with respect to phase in a 10Gbps, single channel, dispersion uncompensated telecommunication system was studied. The characteristic feature of periodic soliton interaction was noted at the Interaction point (I=6202.5Km) in one collision length of L=12405.1 Km. The interaction point is located for 10Gbps system with an initial relative spacing (qo) of soliton as 5.28 using Perturbation theory. It is shown that, when two in-phase solitons are launched, they interact at the point I=6202.5 Km, but the interaction could be restricted with introduction of different phase initially. When the phase of the input solitons increases, the deviation of soliton pulses at the ‘I’ also increases. We have successfully demonstrated this effect in a telecommunication set-up in terms of Quality factor (Q), where the Q=0 for in-phase soliton. The Q was noted to be 125.9, 38.63, 47.53, 59.60, 161.37, and 78.04 for different phases such as 10o, 20o, 30o, 45o, 60o and 90o degrees respectively at Interaction point (I).
Keywords: Soliton interaction, Initial relative spacing, phase, Perturbation theory and telecommunication system.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1696
1134 Traveling Wave Solutions for the Sawada-Kotera-Kadomtsev-Petviashivili Equation and the Bogoyavlensky-Konoplechenko Equation by (G'/G)- Expansion Method
Authors: Nisha Goyal, R.K. Gupta
This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.
Keywords: Sawada-Kotera-Kadomtsev-Petviashivili equation, Bogoyavlensky-Konoplechenko equation,Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1495
1133 New Application of EHTA for the Generalized(2+1)-Dimensional Nonlinear Evolution Equations
Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi
In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota-s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented.
Keywords: EHTA, (2+1)-dimensional CBS equations, (2+1)-dimensional breaking solution equation, Hirota's bilinear form.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1341
1132 Wave Vortex Parameters as an Indicator of Breaking Intensity
Authors: B. Robertson, K. Hall
The study of the geometric shape of the plunging wave enclosed vortices as a possible indicator for the breaking intensity of ocean waves has been ongoing for almost 50 years with limited success. This paper investigates the validity of using the vortex ratio and vortex angle as methods of predicting breaking intensity. Previously published works on vortex parameters, based on regular wave flume results or solitary wave theory, present contradictory results and conclusions. Through the first complete analysis of field collected irregular wave breaking vortex parameters it is illustrated that the vortex ratio and vortex angle cannot be accurately predicted using standard breaking wave characteristics and hence are not suggested as a possible indicator for breaking intensity.
Keywords: Breaking Wave Measurement, Wave Vortex Parameters, Analytical Techniques, Ocean Remote Sensing.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1598
1131 Two-Dimensional Solitary Wave Solution to the Quadratic Nonlinear Schrdinger Equation
Authors: Sarun Phibanchon
The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.
Keywords: soliton, iterative method, spectral method, plasmaProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1744
1130 Soliton Interaction in Birefringent Fibers with Third-Order Dispersion
Authors: Dowluru Ravi Kumar, Bhima Prabhakara Rao
Propagation of solitons in single-mode birefringent fibers is considered under the presence of third-order dispersion (TOD). The behavior of two neighboring solitons and their interaction is investigated under the presence of third-order dispersion with different group velocity dispersion (GVD) parameters. It is found that third-order dispersion makes the resultant soliton to deviate from its ideal position and increases the interaction between adjacent soliton pulses. It is also observed that this deviation due to third-order dispersion is considerably small when the optical pulse propagates at wavelengths relatively far from the zerodispersion. Modified coupled nonlinear Schrödinger-s equations (CNLSE) representing the propagation of optical pulse in single mode fiber with TOD are solved using split-step Fourier algorithm. The results presented in this paper reveal that the third-order dispersion can substantially increase the interaction between the solitons, but large group velocity dispersion reduces the interaction between neighboring solitons.
Keywords: Birefringence, Group velocity dispersion, Polarization mode dispersion, Soliton interaction, Third order dispersion.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1107
1129 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t
Authors: Ahmet Tekcan, Betül Gezer, Osman Bizim
Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.
Keywords: Pell equation, Diophantine equation.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2193
1128 Dust Acoustic Shock Waves in Coupled Dusty Plasmas with Kappa-Distributed Ions
Authors: Hamid Reza Pakzad
We have considered an unmagnetized dusty plasma system consisting of ions obeying superthermal distribution and strongly coupled negatively charged dust. We have used reductive perturbation method and derived the Kordeweg-de Vries-Burgers (KdV-Burgers) equation. The behavior of the shock waves in the plasma has been investigated.
Keywords: Shock, Soliton, Coupling, Superthermal ions.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1786
1127 The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4
Authors: Armend Sh. Shabani
Abstract:Let D ≠ 1 be a positive non-square integer. In this paper are given the proofs for two conjectures related to Pell-s equation x2 -Dy2 = ± 4, proposed by A. Tekcan.
Keywords: Pell's equation, solutions of Pell's equation.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1120
1126 Time Independent Behavior of Tomato Paste
Authors: A. Heidarinasab, V. Moghaddam Nansa
Abstract:This paper deals with rheological behavior of tomato paste from the view point of time independent properties inclusive of processing variables such as sample temperature which influence on rheological properties as well as breaking temperature and concentration which beside the rheological properties, influence on the quality of final product. With this aim 10 tomato paste samples at various concentrations (17-25%) and breaking temperatures (65- 85 C o ) have been produced. The experimental results showed tomato paste behaves as a non-Newtonian semi-fluid which follows power law model that consistency coefficient (K) is supposed function of breaking temperature, concentration and sample temperature with consideration to superimpose function.
Keywords: Breaking temperature, Concentration, Power law, Rheology, Time independent.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3248
1125 An Analytical Method for Solving General Riccati Equation
Authors: Y. Pala, M. O. Ertas
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, ordinary differential equation, nonlinear differential equation, analytical solution, proper solution.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1872
1124 The Pell Equation x2 − Py2 = Q
Authors: Ahmet Tekcan, Arzu Özkoç, Canan Kocapınar, Hatice Alkan
Abstract:Let p be a prime number such that p ≡ 1(mod 4), say p = 1+4k for a positive integer k. Let P = 2k + 1 and Q = k2. In this paper, we consider the integer solutions of the Pell equation x2-Py2 = Q over Z and also over finite fields Fp. Also we deduce some relations on the integer solutions (xn, yn) of it.
Keywords: Pell equation, solutions of Pell equation.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1961
1123 Breaking of Charge Independence of Nucleon-Nucleon Interaction Using Phase Shift Calculations
Authors: B. Rezaei, N. Amiri, N. Azizi
Using calculated phase- shift values, for pp, nn, and np elastic scattering in the energy range 1MeV to 350MeV, the charge independence breaking of nucleon-nucleon interaction is investigated. We have used Darboux transformation to calculate phase-shift for the first three values of
Keywords: Phase-shift, charge independence breaking, Darboux transformation.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1415
1122 The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp
Authors: Ahmet Tekcan, Arzu Özkoç, Hatice Alkan
Abstract:In this work, we consider the number of integer solutions of Diophantine equation D : y2 - 2yx - 3 = 0 over Z and also over finite fields Fp for primes p ≥ 5. Later we determine the number of rational points on curves Ep : y2 = Pp(x) = yp 1 + yp 2 over Fp, where y1 and y2 are the roots of D. Also we give a formula for the sum of x- and y-coordinates of all rational points (x, y) on Ep over Fp.
Keywords: Diophantine equation, Pell equation, quadratic form.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1163
1121 Solution of The KdV Equation with Asymptotic Degeneracy
Authors: Tapas Kumar Sinha, Joseph Mathew
Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung  have given the solution of the KdV equation  to the boundary condition , where b is a constant. We have further extended the method of  to find the solution of the KdV equation with asymptotic degeneracy. Via simulations we find both bright and dark Solitons (i.e. Solitons with opposite phases).
Keywords: KdV equation, Asymptotic Degeneracy, Solitons, Inverse ScatteringProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1462
1120 Nonlinear Propagation of Acoustic Soliton Waves in Dense Quantum Electron-Positron Magnetoplasma
Authors: A. Abdikian
Abstract:Propagation of nonlinear acoustic wave in dense electron-positron (e-p) plasmas in the presence of an external magnetic field and stationary ions (to neutralize the plasma background) is studied. By means of the quantum hydrodynamics model and applying the reductive perturbation method, the Zakharov-Kuznetsov equation is derived. Using the bifurcation theory of planar dynamical systems, the compressive structure of electrostatic solitary wave and periodic travelling waves is found. The numerical results show how the ion density ratio, the ion cyclotron frequency, and the direction cosines of the wave vector affect the nonlinear electrostatic travelling waves. The obtained results may be useful to better understand the obliquely nonlinear electrostatic travelling wave of small amplitude localized structures in dense magnetized quantum e-p plasmas and may be applicable to study the particle and energy transport mechanism in compact stars such as the interior of massive white dwarfs etc.
Keywords: Bifurcation theory, magnetized electron-positron plasma, phase portrait, the Zakharov-Kuznetsov equation.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1064
1119 Exact Solutions of the Helmholtz equation via the Nikiforov-Uvarov Method
Authors: Said Laachir, Aziz Laaribi
The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.
Keywords: Helmholtz equation, Nikiforov-Uvarov method, exact solutions, eigenfunctions.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2869
1118 Study of Cahn-Hilliard Equation to Simulate Phase Separation
Authors: Nara Guimarães, Marcelo Aquino Martorano, Douglas Gouvêa
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1727
1117 Transient Population Dynamics of Phase Singularities in 2D Beeler-Reuter Model
Authors: Hidetoshi Konno, Akio Suzuki
The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-dependent transition rate is given. Then, the exact solution of the mean field equation for the nonlinear Langevin equation is also given. It is demonstrated that transient population dynamics is successfully identified by the generalized Logistic equation with fractional higher order nonlinear term. It is also demonstrated the necessity of introducing time-dependent transition rate in the master equation approach to incorporate the effect of nonlinearity.
Keywords: Transient population dynamics, Phase singularity, Birth-death process, Non-stationary Master equation, nonlinear Langevin equation, generalized Logistic equation.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1458