改进的指数函数方法求时空分数阶混合(1+1)维KdV方程的新精确解

New exact solutions of the space-time fractional mixed kdv equation using the improved exponential function-expansion method

借助修正的Riemann-Liouvielle分数阶导数,采用了改进的指数函数展开法,得到了时空分数阶混合(1+1)维KdV方程的新精确解。先将时空分数阶混合(1+1)维KdV方程转化为整数阶方程;其次引入新的辅助常微分方程,得到方程在不同约束条件下的新精确解,最后对具有代表性的第一种情形下的新解进行了计算机仿真。

By using Riemann-Liouville fractional derivative and applying the improved Exponential function-expansion method, some new exact solutions of space-time fractional mixed KdV equation are obtained.At first, space-time fractional mixed KdV equation can be converted into the non-fractional ordinary differential equation.Later, a new auxiliary ordinary differential equantion is introduced, and some new exact solutions of space-time fractional mixed KdV equation under different constraints are constructed.At last, the new solution under the first representative case is simulated by computer.