基于双曲函数法的五阶非线性演化方程显示行波解

Explicit traveling wave solutions of fifth-order nonlinear evolution equation with the help of hyperbolic function

利用双曲函数方法对Mikhauilov-Novikov-Wang方程的约化情形进行了研究。通过行波约化,将五阶非线性演化方程转为成一个ODE。结合Riccati方程的性质,得到一个关于若干参变量的代数系统,借助于Mathematica符号计算功能,最终得到了上述方程的显示行波解,包括类孤子解、三角函数周期解和有理解。

In this paper, the reduction of Mikhauilov-Novikov-Wang equation is studied by using the hyperbolic function method. By traveling wave reduction, the fifth-order nonlinear evolution equation is transformed into an ODE. Combining with the properties of Riccati equation, an algebraic system of some parameters is obtained. With the help of Mathematica symbolic computing function, the explicit traveling wave solutions of the above equation, including soliton-like solutions, triangular periodic solutions and rational solutions, are finally obtained.