| In this paper,the exact solutions and mixed solutions of several nonlinear wave equations are studied by using Darboux transform method,symbolic calculation method and the simplified form of the Hirota bilinear method.The main work in this paper is as follows:(1)Two five-component nonlinear systems with arbitrary functions are prensented,and their Lax pair and conservation law are discussed.By Darboux transformation method,the exact solutions of its reduced four-component reaction-diffusion equation and four-component generalized coupled m Kd V equation are obtained,and the characteristics of these solutions are given by Mathematica.(2)Using symbolic computation approach,new accelerated rouge wave solution of a complex nonlinear wave equation is constructed.The accelerated rouge wave solution contains an arbitrary function,which can produce some interesting topological properties.Through numerical simulation,the dynamic behaviors of kink-rouge wave,soliton-rouge wave and periodic-rouge wave are systematically analyzed.In addition,Ma breather solution and Akhmediev breather solution of the complex nonlinear wave equation are obtained.(3)By the simplified form of the Hirota bilinear method,the multi-soliton solutions of the(2+1)-dimensional Date-Jimbo-KashiwaraMiwa(DJKM)equation and the(3+1)-dimensional generalized B-type Kadomtsev-Petviashvili(g BKP)equation are given.The long-wave limit is applied to the multi-soliton solutions and the complex conjugate relation of the multi-soliton solutions parameters are selected,the mixed solutions of the high-dimensional nonlinear equations are constructed.The dynamical behaviors of the hybrid solutions are systematically analyzed by numerical simulations. |
