积分微分KP层次方程的精确行波解

对KP层次方程进行积分变换和行波变换得到常微分方程,利用扩展试验方程法把求解常微分方程的问题转化为求解代数方程组的问题,根据不同情况得到了KP层次方程的钟状解、三角函数解、双曲函数解和椭圆函数解的精确表达式,这些解的显示表达式是首次求出的.这种方法对于求解非线性偏微分方程十分有效并且能够得到许多新的精确解.

The Exact Traveling Wave Solution of the Integral Differential KP Hierarchy Equation

By means of the integral transformation and traveling wave transformation, the KP hierarchical equation can be turned into the equivalent ordinary differential equation. With the help of the extended trial equation method, the problem of solving ordinary differential equation is transformed into that of solving algebraic equation system. According to the solutions of algebraic equation system and the extended trial equation, we have obtained the exact expressions of bell-shaped solution, triangular solution, hyperbolic solution and elliptic function solution of the KP hierarchical equation. The explicit expressions of these solutions are obtained for the first time. With the extended trial equation method, many new exact solutions of nonlinear partial differential equations can be obtained effectively.