scholarly journals Method for Studying the Multisoliton Solutions of the Korteweg-de Vries Type Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Yuriy Turbal ◽  
Andriy Bomba ◽  
Mariana Turbal
Keyword(s):  
Soliton Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
New Approach ◽  
Wave Solutions ◽  
De Vries ◽  
Multisoliton Solutions

We present a new approach to find travelling wave solutions for the Korteweg-de Vries type equations, which allows extending the class of known soliton solutions. Also we propose method for studying the multisoliton solutions of the Korteweg-de Vries type equations.

Bright soliton solutions, power series solutions and travelling wave solutions of a (3+1)-dimensional modified Korteweg–de Vries–Kadomtsev–Petviashvili equation

2018 ◽  
Vol 32 (06) ◽  
pp. 1850082
Author(s):  
Ding Guo ◽  
Shou-Fu Tian ◽  
Li Zou ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Bright Soliton ◽  
Travelling Wave Solutions ◽  
Series Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Power Series Solutions ◽  
De Vries

In this paper, we consider the (3[Formula: see text]+[Formula: see text]1)-dimensional modified Korteweg–de Vries–Kadomtsev–Petviashvili (mKdV-KP) equation, which can be used to describe the nonlinear waves in plasma physics and fluid dynamics. By using solitary wave ansatz in the form of sech[Formula: see text] function and a direct integrating way, we construct the exact bright soliton solutions and the travelling wave solutions of the equation, respectively. Moreover, we obtain its power series solutions with the convergence analysis. It is hoped that our results can provide the richer dynamical behavior of the KdV-type and KP-type equations.

Three Kind of Triangle Rational Functions and Applications for Discrete Nonlinear Equations

2011 ◽  
Vol 317-319 ◽  
pp. 2168-2171
Author(s):  
Xiu Rong Guo ◽  
Zheng Tao Liu ◽  
Mei Guo
Keyword(s):  
Nonlinear Equations ◽  
Difference Equations ◽  
Soliton Solutions ◽  
Rational Functions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Periodic Travelling Wave ◽  
Formal Solutions

In order to efficiently search for new soliton solutions to differential-difference equations (DDEs), three kinds of triangle rational functions are first introduced. Then a kind of formal solutions of DDEs are presented which are expressed by a unified nonlinear combination of the three kinds of triangle rational functions. As illustrative examples, the periodic travelling-wave solutions of the discrete modified KdV(mKdV) equations are obtained.

New Soliton Solutions of Chaffee-Infante Equations Using the Exp-Function Method

2010 ◽  
Vol 65 (3) ◽  
pp. 197-202 ◽  
Author(s):  
Rathinasamy Sakthivel ◽  
Changbum Chun
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symbolic Computation ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

In this paper, the exp-function method is applied by using symbolic computation to construct a variety of new generalized solitonary solutions for the Chaffee-Infante equation with distinct physical structures. The results reveal that the exp-function method is suited for finding travelling wave solutions of nonlinear partial differential equations arising in mathematical physics

Symbolic Computation and Non-travelling Wave Solutions of the (2+1)-Dimensional Korteweg de Vries Equation

2005 ◽  
Vol 60 (4) ◽  
pp. 221-228 ◽  
Author(s):  
Dengshan Wang ◽  
Hong-Qing Zhang
Keyword(s):  
Symbolic Computation ◽  
Evolution Equations ◽  
Vries Equation ◽  
Expansion Method ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Jacobi Elliptic Function ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
De Vries

Abstract In this paper, with the aid of symbolic computation we improve the extended F-expansion method described in Chaos, Solitons and Fractals 22, 111 (2004) to solve the (2+1)-dimensional Korteweg de Vries equation. Using this method, we derive many exact non-travelling wave solutions. These are more general than the previous solutions derived with the extended F-expansion method. They include the Jacobi elliptic function, soliton-like trigonometric function solutions, and so on. Our method can be applied to other nonlinear evolution equations.

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