非线性色散耗散mKdv方程的Riccati函数解

Riccati function solutions of nonlinear dispersive-dissipative mKdv equation

对mKdv方程进行了扩展,得到非线性色散耗散mKdv方程:ut+αu2ux+βuxx+γuxxx=0.从解的形式和约束条件两个方面对求解非线性数学物理方程的F-展开法进行了改进,得到广义扩展的F-展开法.借助于广义扩展的F-展开法和计算机符号系统Mathematica,求出了非线性色散耗散mKdv方程的一系列类型丰富的Riccati函数精确解,包含了周期波解、类孤子解、三角函数解、有理函数解、复数形式解等.

The mKdv equation is expanded and a nonlinear dispersive dissipative mKdv equation is obtained as ：ut＋α u2ux＋βuxx＋γuxxx=0.The generalized modified F-expansion method is developed to solve nonlinear mathematic physic equations. This method is improved by F-expansion method in the form of solution and constraint condition. By using the generalized modified F-expansion method and with the aid of computer symbolism system Mathematica,abundant exact solutions of the nonlinear dispersive dissipative mKdv equation are obtained,including single and combined non-degenerate Jacobi elliptic function solutions,soliton-like solutions,exponential solutions,periodic wave solutions,solitary wave solutions,triangle function solutions,rational function solutions,and plural number formal solutions,etc.