A unified trial function method in finding the explicit and exact solutions to three NPDEs

Xie Y; Tang JS

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A unified trial function method in finding the explicit and exact solutions to three NPDEs

机译：寻找三个NPDE的明确和精确解的统一试验函数方法

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In this paper, by introducing a transformation and utilizing the trial function method, it is quite interesting that three nonlinear partial differential equations called the KdV equation, Boussinesq equation and CDGSK equation have exactly the same trial function form and that their explicit and exact solutions which include solitary wave solutions, singular travelling wave solutions, and triangle function-type periodic wave solutions can be easily derived in a unified and concise way. Among them, some are new travelling wave solutions of physical interest.

机译：在本文中，通过介绍一种变换并利用试算函数方法，很有趣的是，三个非线性偏微分方程KdV方程，Boussinesq方程和CDGSK方程具有完全相同的试函数形式，并且它们的显式和精确解能够包括孤立波解，奇异行波解和三角函数型周期波解可以很容易地以统一和简洁的方式导出。其中，一些是具有实际意义的新行波解决方案。

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《Physica Scripta: An International Journal for Experimental and Theoretical Physics》 |2006年第2期|共4页
作者
Xie Y; Tang JS;
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原文格式 PDF
正文语种 eng
中图分类物理学;
关键词
JACOBI ELLIPTIC FUNCTION; FUNCTION EXPANSION METHOD; NONLINEAR-WAVE EQUATIONS; PERIODIC-SOLUTIONS; SHALLOW-WATER; LONG WAVES;

机译：雅各比椭圆函数;函数展开法;非线性波动方程;周期解;浅水;长波;

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1. A unified trial function method in finding the explicit and exact solutions to three NPDEs [J] . Xie Y, Tang JS Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2006,第2期

机译：寻找三个NPDE的明确和精确解的统一试验函数方法
2. A new generalized expansion method and its application in finding explicit exact solutions for a generalized variable coefficients KdV equation [J] . Sabry R, Zahran MA, Fan EG Physics Letters, A . 2004,第1a2期

机译：一种新的广义展开方法及其在寻找广义变系数KdV方程的显式精确解中的应用
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A unified trial function method in finding the explicit and exact solutions to three NPDEs

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