**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1491

# Search results for: Coupled Korteweg-de Vries(KdV) equation

##### 1491 Numerical Study of Some Coupled PDEs by using Differential Transformation Method

**Authors:**
Reza Abazari,
Rasool Abazari

**Abstract:**

In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.

**Keywords:**
Coupled Korteweg-de Vries(KdV) equation,
Coupled Burgers equation,
Coupled Schrödinger equation,
differential transformation method.

##### 1490 An H1-Galerkin Mixed Method for the Coupled Burgers Equation

**Authors:**
Xianbiao Jia,
Hong Li,
Yang Liu,
Zhichao Fang

**Abstract:**

In this paper, an H1-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived.

**Keywords:**
The coupled Burgers equation,
H1-Galerkin mixed
finite element method,
Backward Euler's method,
Optimal error
estimates.

##### 1489 Constructing Distinct Kinds of Solutions for the Time-Dependent Coefficients Coupled Klein-Gordon-Schrödinger Equation

**Authors:**
Anupma Bansal

**Abstract:**

We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.

**Keywords:**
Klein-Gordon-Schödinger Equation,
Lie Classical Method,
Exact Solutions

##### 1488 Mathematical Approach for Large Deformation Analysis of the Stiffened Coupled Shear Walls

**Authors:**
M. J. Fadaee,
H. Saffari,
H. Khosravi

**Abstract:**

**Keywords:**
Buckling load,
differential equation,
energy method,
geometrically nonlinear analysis,
mathematical method,
Stiffened
coupled shear walls.

##### 1487 A Novel System of Two Coupled Equations for the Longitudinal Components of the Electromagnetic Field in a Waveguide

**Authors:**
Arti Vaish,
Harish Parthasarathy

**Abstract:**

**Keywords:**
Electromagnetism,
Maxwell's Equations,
Anisotropic permittivity,
Wave equation,
Matrix Equation,
Permittivity tensor.

##### 1486 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t

**Authors:**
Ahmet Tekcan,
Betül Gezer,
Osman Bizim

**Abstract:**

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.

##### 1485 Mathematical Modelling of Transport Phenomena in Radioactive Waste-Cement-Bentonite Matrix

**Authors:**
Ilija Plecas,
Uranija Kozmidis-Luburic,
Radojica Pesic

**Abstract:**

The leaching rate of 137Cs from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source an equation for diffusion coupled to a firstorder equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

**Keywords:**
bentonite,
cement ,
radioactive waste,
composite,
disposal,
diffusion

##### 1484 Dust Acoustic Shock Waves in Coupled Dusty Plasmas with Kappa-Distributed Ions

**Authors:**
Hamid Reza Pakzad

**Abstract:**

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.

##### 1483 The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4

**Authors:**
Armend Sh. Shabani

**Abstract:**

**Keywords:**
Pell's equation,
solutions of Pell's equation.

##### 1482 DQ Analysis of 3D Natural Convection in an Inclined Cavity Using an Velocity-Vorticity Formulation

**Abstract:**

In this paper, the differential quadrature method is applied to simulate natural convection in an inclined cubic cavity using velocity-vorticity formulation. The numerical capability of the present algorithm is demonstrated by application to natural convection in an inclined cubic cavity. The velocity Poisson equations, the vorticity transport equations and the energy equation are all solved as a coupled system of equations for the seven field variables consisting of three velocities, three vorticities and temperature. The coupled equations are simultaneously solved by imposing the vorticity definition at boundary without requiring the explicit specification of the vorticity boundary conditions. Test results obtained for an inclined cubic cavity with different angle of inclinations for Rayleigh number equal to 103, 104, 105 and 106 indicate that the present coupled solution algorithm could predict the benchmark results for temperature and flow fields. Thus, it is convinced that the present formulation is capable of solving coupled Navier-Stokes equations effectively and accurately.

**Keywords:**
Natural convection,
velocity-vorticity formulation,
differential quadrature (DQ).

##### 1481 An Analytical Method for Solving General Riccati Equation

**Authors:**
Y. Pala,
M. O. Ertas

**Abstract:**

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.

##### 1480 The Pell Equation x2 − Py2 = Q

**Authors:**
Ahmet Tekcan,
Arzu Özkoç,
Canan Kocapınar,
Hatice Alkan

**Abstract:**

**Keywords:**
Pell equation,
solutions of Pell equation.

##### 1479 The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp

**Authors:**
Ahmet Tekcan,
Arzu Özkoç,
Hatice Alkan

**Abstract:**

**Keywords:**
Diophantine equation,
Pell equation,
quadratic form.

##### 1478 Equations of Pulse Propagation in Three-Layer Structure of As2S3 Chalcogenide Plasmonic Nano-Waveguides

**Authors:**
Leila Motamed-Jahromi,
Mohsen Hatami,
Alireza Keshavarz

**Abstract:**

This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As_{2}S_{3} chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

**Keywords:**
Nonlinear optics,
propagation equation,
plasmonic waveguide.

##### 1477 Solution of The KdV Equation with Asymptotic Degeneracy

**Authors:**
Tapas Kumar Sinha,
Joseph Mathew

**Abstract:**

Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung [2] have given the solution of the KdV equation [1] to the boundary condition , where b is a constant. We have further extended the method of [2] 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 Scattering

##### 1476 Exact Solutions of the Helmholtz equation via the Nikiforov-Uvarov Method

**Authors:**
Said Laachir,
Aziz Laaribi

**Abstract:**

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.

##### 1475 Study of Cahn-Hilliard Equation to Simulate Phase Separation

**Authors:**
Nara Guimarães,
Marcelo Aquino Martorano,
Douglas Gouvêa

**Abstract:**

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.

##### 1474 A New Microstrip Diplexer Using Coupled Stepped Impedance Resonators

**Authors:**
A. Chinig,
J. Zbitou,
A. Errkik,
L. Elabdellaoui,
A. Tajmouati,
A. Tribak,
M. Latrach

**Abstract:**

This paper presents a new structure of microstrip band pass filter (BPF) based on coupled stepped impedance resonators. Each filter consists of two coupled stepped impedance resonators connected to microstrip feed lines. The coupled junction is utilized to connect the two BPFs to the antenna. This two band pass filters are designed and simulated to operate for the digital communication system (DCS) and Industrial Scientific and Medical (ISM) bands at 1.8 GHz and 2.45 GHz respectively. The proposed circuit presents good performances with an insertion loss lower than 2.3 dB and isolation between the two channels greater than 21 dB. The prototype of the optimized diplexer have been investigated numerically by using ADS Agilent and verified with CST microwave software.

**Keywords:**
Band Pass Filter,
coupled junction,
coupled stepped
impedance resonators,
diplexer,
insertion loss,
isolation.

##### 1473 Transient Population Dynamics of Phase Singularities in 2D Beeler-Reuter Model

**Authors:**
Hidetoshi Konno,
Akio Suzuki

**Abstract:**

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.

##### 1472 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

**Abstract:**

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,

##### 1471 Stability of Fractional Differential Equation

**Authors:**
Rabha W. Ibrahim

**Abstract:**

We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.

**Keywords:**
Fractional calculus,
fractional differential equation,
Lane-Emden equation,
Riemann-Liouville fractional operators,
Volterra integral equation.

##### 1470 Traveling Wave Solutions for Shallow Water Wave Equation by (G'/G)-Expansion Method

**Authors:**
Anjali Verma,
Ram Jiwari,
Jitender Kumar

**Abstract:**

This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.

**Keywords:**
Shallow water wave equation,
Exact solutions,
(G'/G) expansion method.

##### 1469 Existence of Iterative Cauchy Fractional Differential Equation

**Authors:**
Rabha W. Ibrahim

**Abstract:**

Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.

**Keywords:**
Fractional calculus,
fractional differential equation,
Cauchy equation,
Riemann-Liouville fractional operators,
Volterra
integral equation,
non-expansive mapping,
iterative differential equation.

##### 1468 FWM Wavelength Conversion Analysis in a 3-Integrated Portion SOA and DFB Laser using Coupled Wave Approach and FD-BPM Method

**Authors:**
M. K. Moazzam,
A. Salmanpour,
M. Nirouei

**Abstract:**

**Keywords:**
distributed feedback laser,
nondegenerate fourwave mixing,
semiconductor optical amplifier,
wavelengthconversion

##### 1467 Ginzburg-Landau Model for Curved Two-Phase Shallow Mixing Layers

**Authors:**
Irina Eglite,
Andrei A. Kolyshkin

**Abstract:**

**Keywords:**
Shallow water equations,
mixing layer,
weakly
nonlinear analysis,
Ginzburg-Landau equation

##### 1466 Transient Combined Conduction and Radiation in a Two-Dimensional Participating Cylinder in Presence of Heat Generation

**Authors:**
Raoudha Chaabane,
Faouzi Askri,
Sassi Ben Nasrallah

**Abstract:**

**Keywords:**
heat generation,
cylindrical coordinates; RTE;transient; coupled conduction radiation; heat transfer; CVFEM; LBM

##### 1465 Analytical Investigation of the Effects of a Standing Ocean Wave in a Wave-Power Device OWC

**Authors:**
E.G. Bautista,
F. Méndez,
O. Bautista,
J.C. Arcos

**Abstract:**

**Keywords:**
Oscillating water column,
Shallow flow,
Waveenergy.

##### 1464 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

**Abstract:**

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.

##### 1463 Coupled Galerkin-DQ Approach for the Transient Analysis of Dam-Reservoir Interaction

**Authors:**
S. A. Eftekhari

**Abstract:**

In this paper, a numerical algorithm using a coupled Galerkin-Differential Quadrature (DQ) method is proposed for the solution of dam-reservoir interaction problem. The governing differential equation of motion of the dam structure is discretized by the Galerkin method and the DQM is used to discretize the fluid domain. The resulting systems of ordinary differential equations are then solved by the Newmark time integration scheme. The mixed scheme combines the simplicity of the Galerkin method and high accuracy and efficiency of the DQ method. Its accuracy and efficiency are demonstrated by comparing the calculated results with those of the existing literature. It is shown that highly accurate results can be obtained using a small number of Galerkin terms and DQM sampling points. The technique presented in this investigation is general and can be used to solve various fluid-structure interaction problems.

**Keywords:**
Dam-reservoir system,
Differential quadrature method,
Fluid-structure interaction,
Galerkin method,
Integral quadrature method.

##### 1462 Conduction Accompanied With Transient Radiative Heat Transfer Using Finite Volume Method

**Authors:**
A. Ashok,
K.Satapathy,
B. Prerana Nashine

**Abstract:**

**Keywords:**
Radiative transfer equation,
finite volume method,
conduction,
transient radiation.