改进的tan■-展开法和几类非线性分数阶发展方程

The Improved tan■-Expansion Method and Several Types of Nonlinear Fractional Evolution Equation

运用改进的tan■-展开法,以一阶常系数微分方程为辅助方程,结合齐次平衡原理,研究了非线性分数阶Khokhlov-Zabolotskaya-Kuznetsov(KZK)方程、非线性分数阶foam drainage方程、非线性分数阶Jimbo-Miwa(JM)方程.借助符号计算系统Maple,求出了方程的多种精确解,这些解包括周期解、孤子解、有理函数解、指数函数解,扩大了解的范围.

Using the improved tan■-expansion method and the first order constant coefficient differential equation as an auxiliary equation,combined with the principle of homogeneous equilibrium,the nonlinear fractional order KZK equation,nonlinear fractional order foam drainage equation,and nonlinear fractional order Jimbo Miwa(JM)eqution are studied.With the aid of coincidence computing system Maple,various exact solutions of the equation are obtained,including periodic solutions,soliton solutions,rational function solutions,and exponential function solutions,expanding the scope of the solution.