非线性方程Klein-Gordon新的行波解

A New Travelling Wave Solution for Nonlinear Klein-Gordon Equation

求非线性波动方程的解的方法有齐次平衡原则,双曲正切函数展开法,试探函数法,非线性变换法,Sine-Cosine展开法,J acobi椭圆函数展开法,F-展开法等。本文利用推行的F-展开法,作变量代换及行波变换得到了Klein-Gordon方程许多新的精确解,包括新的孤立子波解,该方法为求解类似的方程提供了借鉴。

There are many ways to get the solutions for nonlinear wave equation, such as homogeneous balance principle, hyperbolic tangent function expansion, tentative function method, nonlinear transformation, Sine - Cosine expansion, Jacobi elliptic function expansion, F - expansion and so on. This paper gets many new exact solutions for Klein - Gordon equation by employing variable substitution and travelling wave transformation with the help of modified F - expansion. The result includes some new solitary wave solutions. The methods used in this paper give good examples for the solution of similar equations.