(3+1)维时空分数阶偏微分方程mKdV-ZK方程的新精确解

New exact solutions for the (3+1)-dimensional space-time fractional mKdV-ZK equation

摘要:

(3+1)维时空分数阶偏微分方程mKdV-ZK方程精确解的构建重要而令人感兴趣.本文通过含三维空间、一维时间的分数阶复变换将分数阶mKdV-ZK 方程转化为非线性常微分方程,再引入新的辅助微分方程的解及其新的展开形式,构建了mKdV-ZK方程系列精确解.

Abstract:

It is very important and interesting to construct the exact solutions of the (3+1)-dimensional space-time fractional mKdV-ZK equation.Firstly, by using fractional complex transformation, mKdV-ZK equation was transformed into a nonlinear ordinary deferential equation, and then introducing extends (G'/G)-expansion method to construct the exact solution. A series of new exact solution for mKdV-ZK equations have been obtained.