Exact Solutions Of One Type Nonlinear Evolution Equations

It is more simple and effective for us to find the exact solutions of some nonlinear evolution equations which use invariant subspace method. This paper mainly studies the polynomial so-lutions of the (2+1)-dimensional variable coefficient dispersionless Kadomtsev-Petiashili (dKP)equation. More trivial solutions and hyperspace blow-up solutions of the (3+1)-dimensional dKP equation will be obtained in case of adding one dimension. The results of this paper gener-alize the application of the method of invariant subspace in the solutions of the high dimensional partial differential equations.The general outline of this abstract is as follows:Chapter 1 is the introduction which mainly recommends the research background and the relevant knowledge of using invariant subspace method solving some exact solutions.In chapter 2, the KP equation is introduced firstly, and then the polynomial solutions are given.In chapter 3, the trivial solutions and the hyperspace blow-up solutions of (3+1)-dimensional dKP equation are studied firstly, then we can directly give the exact solutions of the (3+1)-dimensional KZK equation by the value of p(t) through the theorems.The last chapter makes a summary and then the follow-up work is forecasted.