A new elliptic equation rational expansion method and its application to the shallow long wave approximate equations

Yong Chen; Qi Wang

doi:10.1016/j.amc.2005.04.061

A new elliptic equation rational expansion method and its application to the shallow long wave approximate equations

Yong Chen^*
, Qi Wang

^*Corresponding author for this work

Ningbo University
Shanghai Jiao Tong University
Chinese Academy of Sciences
Dalian University of Technology

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

A new elliptic equation rational expansion method is presented by a new general ansätz, which is a direct and unified algebraic method for constructing multiple and more general travelling wave solution for nonlinear partial differential equation and implemented in a computer algebraic system. The proposed method is applied to consider the shallow long wave approximate equation and obtains rich new families of the exact solutions, including rational form solitary wave, rational form triangular periodic, rational form Jacobi and Weierstrass doubly periodic solutions.

Original language	English
Pages (from-to)	1163-1182
Number of pages	20
Journal	Applied Mathematics and Computation
Volume	173
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2005.04.061
State	Published - 15 Feb 2006
Externally published	Yes

Keywords

Elliptic equation rational expansion method
Rational form solitary wave solutions
Shallow long wave approximate equation
Travelling wave solution

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10.1016/j.amc.2005.04.061

Cite this

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abstract = "A new elliptic equation rational expansion method is presented by a new general ans{\"a}tz, which is a direct and unified algebraic method for constructing multiple and more general travelling wave solution for nonlinear partial differential equation and implemented in a computer algebraic system. The proposed method is applied to consider the shallow long wave approximate equation and obtains rich new families of the exact solutions, including rational form solitary wave, rational form triangular periodic, rational form Jacobi and Weierstrass doubly periodic solutions.",

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AB - A new elliptic equation rational expansion method is presented by a new general ansätz, which is a direct and unified algebraic method for constructing multiple and more general travelling wave solution for nonlinear partial differential equation and implemented in a computer algebraic system. The proposed method is applied to consider the shallow long wave approximate equation and obtains rich new families of the exact solutions, including rational form solitary wave, rational form triangular periodic, rational form Jacobi and Weierstrass doubly periodic solutions.

KW - Elliptic equation rational expansion method

KW - Rational form solitary wave solutions

KW - Shallow long wave approximate equation

KW - Travelling wave solution

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A new elliptic equation rational expansion method and its application to the shallow long wave approximate equations

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Keywords

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