scholarly journals The Double Auxiliary Equations Method and its Application to Some Nonlinear Evolution Equations

2019 ◽  
pp. 1-11 ◽  
Author(s):  
A. A. Moussa ◽  
I. M. E. Abdelstar ◽  
A. K. Osman ◽  
L. A. Alhakim
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Schrodinger Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Evolution Equations ◽  
New Method ◽  
Long Wave ◽  
Rlw Equation

Throughout this article, symbolic computation will be used in order to construct a more general exact solutions of the nonlinear evolution equations through a new method called the double auxiliary equations' method, the method represent the study focus of this article. The method has proven applicable and practical through its applications to the generalized regularized long wave (RLW) equation and nonlinear Schrodinger equation.

scholarly journals New Soliton-like Solutions of Variable Coefficient Nonlinear Schrödinger Equations

2004 ◽  
Vol 59 (4-5) ◽  
pp. 196-202 ◽  
Author(s):  
Heng-Nong Xuan ◽  
Changji Wang ◽  
Dafang Zhang
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Schrödinger ◽  
System Method ◽  
Nonlinear Schrodinger Equations

The improved projective Riccati system method for solving nonlinear evolution equations (NEEs) is established. With the help of symbolic computation, one can obtain more exact solutions of some NEEs. To illustrate the method, we take the variable coefficient nonlinear Schrödinger equation as an example, and obtain four families of soliton-like solutions. Eight figures are given to illustrate some features of these solutions.

The Exp-function Method for the Riccati Equation and Exact Solutions of Dispersive Long Wave Equations

2008 ◽  
Vol 63 (10-11) ◽  
pp. 663-670 ◽  
Author(s):  
Sheng Zhang ◽  
Wei Wang ◽  
Jing-Lin Tong
Keyword(s):  
Exact Solutions ◽  
Riccati Equation ◽  
Function Method ◽  
Wave Equations ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Mathematical Tool ◽  
New Exact Solutions ◽  
Long Wave

In this paper, the Exp-function method is used to seek new generalized solitonary solutions of the Riccati equation. Based on the Riccati equation and one of its generalized solitonary solutions, new exact solutions with three arbitrary functions of the (2+1)-dimensional dispersive long wave equations are obtained. Compared with the tanh-function method and its extensions, the proposed method is more powerful. It is shown that the Exp-function method provides a straightforward and important mathematical tool for solving nonlinear evolution equations in mathematical physics.

Notiz: A Symbolic Computation-Based Method and Two Nonlinear Evolution Equations for Water Waves

1997 ◽  
Vol 52 (3) ◽  
pp. 295-296
Author(s):  
Yi-Tian Gao ◽  
Bo Tian
Keyword(s):  
Symbolic Computation ◽  
Solitary Waves ◽  
Water Waves ◽  
Water Wave ◽  
Wave Equations ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Long Wave ◽  
Shallow Water Wave Equations

Abstract A symbolic-computation-based method, which has been newly proposed, is considered for a (2+1)-dimensional generalization of shallow water wave equations and a coupled set of the (2 +1)-dimensional integrable dispersive long wave equations. New sets of soliton-like solutions are constructed, along with solitary waves.

scholarly journals New Jacobi Elliptic Function Solutions for the Zakharov Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yun-Mei Zhao
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobi Elliptic Function

A generalized(G′/G)-expansion method is proposed to seek the exact solutions of nonlinear evolution equations. Being concise and straightforward, this method is applied to the Zakharov equations. As a result, some new Jacobi elliptic function solutions of the Zakharov equations are obtained. This method can also be applied to other nonlinear evolution equations in mathematical physics.

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