Exact Solutions Of Three High Dimensional Nonlinear Partial Differential Equations

This thesis is focused on researching in exact solutions of three equations,(2+1)dimensional Hirota-Satsuma-Ito equation,a kind of(3+1)-dimensional nonlinear evolution equation and a type of extended(3+1)-dimensional Kadomtsev-Petviashvili equation.First,based on Hirota direct method and the homoclinic breather limit method,three types of exact solutions of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,including rogue waves,breather waves and solitary waves.Further,the idea is used to solve a(3+1)-dimensional nonlinear evolution equation and the aforementioned exact solutions are obtained.Finally,in view of Hirota bilinear form,generalized bilinear operator and the method of solitary wave ansatz,the extended(3+1)-dimensional Kadomtsev Petviashvili equation's lump solution,the reduced dimensional lump solution and the bright dark soliton solutions are given.In the process of solving these three equations,the symbolic calculation is carried out with the help of Maple.Moreover,in order to further understand the dynamic behavior of these solutions,through well-chosen parameters,the corresponding graphic simulations are presented,respectively.