试探方程法及其在非线性发展方程中的应用

Trial equation method and its applications to nonlinear evolution equations

提出了一种比较系统的求解非线性发展方程精确解的新方法,即试探方程法.以一个带5阶导数项的非线性发展方程为例,利用试探方程法化成初等积分形式,再利用三阶多项式的完全判别系统求解,由此求得的精确解包括有理函数型解,孤波解,三角函数型周期解,多项式型Jacobi椭圆函数周期解和分式型Jacobi椭圆函数周期解.

A new method, that is, trial equation method, was given to obtain the exact traveling wave solutions for nonlinear evolution equations. As an example, a class of fifth-order nonlinear evolution equations was discussed. Its exact traveling wave solutions, which included rational form solutions, Solitary wave solutions, triangle function periodic solutions, polynomial type Jacobian elliptic function periodic solutions and fractional type Jacobian elliptic function periodic solutions, were given.