New exact travelling wave solutions to the complex coupled KdV equations and modified KdV equation

2008 ◽  
Vol 13 (9) ◽  
pp. 1776-1781 ◽  
Author(s):  
Huiqun Zhang
Keyword(s):  
Kdv Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Kdv Equations ◽  
Wave Solutions ◽  
Modified Kdv Equation ◽  
Coupled Kdv Equations

scholarly journals Classification of Multiply Travelling Wave Solutions for Coupled Burgers, Combined KdV-Modified KdV, and Schrödinger-KdV Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
A. R. Seadawy ◽  
K. El-Rashidy
Keyword(s):  
Differential Equations ◽  
Kdv Equation ◽  
Travelling Waves ◽  
Nonlinear Partial Differential Equations ◽  
Transformation Method ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Kdv Equations ◽  
Wave Solutions ◽  
Equations Of Mathematical Physics

Some explicit travelling wave solutions to constructing exact solutions of nonlinear partial differential equations of mathematical physics are presented. By applying a theory of Frobenius decompositions and, more precisely, by using a transformation method to the coupled Burgers, combined Korteweg-de Vries- (KdV-) modified KdV and Schrödinger-KdV equation is written as bilinear ordinary differential equations and two solutions to describing nonlinear interaction of travelling waves are generated. The properties of the multiple travelling wave solutions are shown by some figures. All solutions are stable and have applications in physics.

scholarly journals Solutions of the perturbed KdV equation for convecting fluids by factorizations

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Octavio Cornejo-Pérez ◽  
Haret Rosu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Kdv Equation ◽  
Travelling Wave ◽  
Second Order ◽  
Travelling Wave Solutions ◽  
Second Order Differential Equation ◽  
Wave Solutions ◽  
Perturbed Kdv Equation

AbstractIn this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential andWeierstrass functions.

Generalized tanh Method Extended to Special Types of Nonlinear Equations

2002 ◽  
Vol 57 (8) ◽  
pp. 692-700 ◽  
Author(s):  
Engui Fan ◽  
Y. C. Hona
Keyword(s):  
Nonlinear Equations ◽  
Gordon Equation ◽  
Kdv Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Sine Gordon Equation ◽  
Wave Solutions ◽  
Tanh Method

By some ‘pre-possessing’ techniques we extend the generalized tanh method to special types of nonlinear equations for constructing their multiple travelling wave solutions. The efficiency of the method can be demonstrated for a large variety of special equations such as those considered in this paper, double sine-Gordon equation, (2+1)-dimensional sine-Gordon equation, Dodd-Bullough- Mikhailov equation, coupled Schrödinger-KdV equation and (2+1)-dimensional coupled Davey- Stewartson equation. - Pacs: 03.40.Kf; 02.30.Jr.

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