非线性分数阶Klein-Gordon方程的新的显式解

New explicit solutions for the nonlinear fractional Klein-Gordon equation

摘要:

本文应用一种新的$(G'/G)$-展开法构建了非线性分数阶Klein-Gordon方程的更多、更一般的精确解.利用分数阶复变换,非线性分数阶Klein-Gordon方程被转化为非线性常微分方程.应用扩展的$(G'/G)$-展开法构建非线性分数阶Klein-Gordon方程精确解.得到了一系列新的显式解,包括双曲函数解,三角函数解和负幂次解,利用该方法获得了比以往更丰富的解.

Abstract:

This paper discuss a new approach of $(G'/G)$-expansion method for constructing more general exact solutions of nonlinear fractional Klein-Gordon equation. By using the fractional complex transformation,the nonlinear fractional Klein-Gordon equation have been converted to nonlinear ordinary differential equation,we will apply the extended $(G'/G)$-expansion method to construct the exact solutions of nonlinear fractional Klein-Gordon equation,a series new explicit solutions were obtained,which include hyperbolic function,trigonometric and negative exponential solutions,more richer than before results.