Solitary Wave Solutions Of Some Nonlinear Reaction-Diffusion Equations And Wave Equations Are Studied

For the past few years,with an increasing number of scholars'in-depth research on nonlinear partial differential equations,a series of solutions were proposed and developed,and many equations were solved.However,due to the limitations of existing methods,there are still many types of equations that have not been reasonably solved up to now,and some equations only have their specific solutions,and more types of solutions need to be further explored.In this paper,we mainly study the solutions of some nonlinear reaction-diffusion equations and wave equations.In the first chapter,the background and development status of nonlinear partial differ-ential equation solving are described,and then the main work arrangement of this paper is given.In the second chapter,the solitary wave solution of the simplified Hodgkin-Huxley equation is studied draw support from Cole-Hopf transformation,and its wave graph is given by Mathematica.some new solutions of Huxley equation and Fitzhugh-Nagumo equation are also obtained when certain values of parameters are given simultaneously.In the third chapter,according to G?/(G+G?)polynomial expansion method,some new solitary wave solutions of Chaffee-Infante equation,another nonlinear reaction diffusion equation,are solved by this method.In the fourth chapter,the solitary wave solutions of two types of nonlinear wave e-quations are researched.One of them is based on the first integral method,which is very important and widely used for a class of nonlinear wave equations u_tt-a₁u_xx+a₂u_t+a₃u+a₄u²+a₅u³=0.On the other hand,the G?/G polynomial expansion method is used to study the solutions of the Mindlin type nonlinear wave model in microstructured solids.