mBBM方程和Vakhnenko方程的显式精确解

Explicit and exact solutions to the mBBM and Vakhnenko equations

应用试探函数方法求解了mBBM方程和Vakhnenko方程。通过引入试探函数,把难于求解的非线性偏微分方程化为易于求解的代数方程,然后用待定系数法确定相应的常数,从而简洁地求得方程的精确解。

The mBBM and Vakhnenko equations are solved by the trial function method. By introducing appropriate trial functions, the nonlinear partial differential equation that is hard to be solved by the usual ways can be reduced to a set of algebraic equation, which can be easily solved, and its related coefficients can be easily determined by the method of undetermined coefficient. Finally, the analytical solution to the equations are successfully derived.