The Research On The Traveling Wave Solution Of Nonlinear Reaction Diffusion Equations

Nowadays, the precise degree of some subjects depends on the analysis ofmathematical models, such as Physics, Biology, Chemistry. Many models can beclassified as nonlinear reaction diffusion equation model. There is a special solution inthe nonlinear reaction diffusion equations, named traveling wave solution, it is a spacetranslation invariant solution. The existence of traveling wave solutions plays animportant part in the diffusion biological population model and the diffusion infectiousdiseases model. In recent years, more and more scholars begin to study the travelingwave solution of nonlinear reaction diffusion equations and its calculation method.Basing on the study by these scholars, have a discussion on the traveling wave solutionof two kinds of models. This paper is composed of four chapters.In the first chapter, we have an overview on the historical and scientificsignificance for the traveling wave solution of nonlinear reaction diffusion equation.Domestic and international status quo are analyzed, preliminary knowledge and themain work of this paper are introduced.In the second chapter, we discuss traveling wave solutions of two types ofdiffusion biological populations: The diffusion Holling–Tanner model and Thediffusion Holling–Tanner model. By the Riccati equation mapping method, we gettraveling wave solutions of the diffusion Holling-Tanner model and the diffusionLotka-Volterra system. we select appropriate parameters, they meet the existenceconditions of the traveling wave solutions, and give the computer numerical simulationas well.In the third chapter, we describes the existence conditions of traveling wavesolutions of two representative diffusion infectious disease models and the minimum wave speed: The diffusion Hepatitis B virus immunization model and the diffusionacute and chronic hepatitis C virus vertical transmission model; we select appropriateparameters, they meet the existence conditions of the traveling wave solutions, andgive the computer numerical simulation as well.In the fourth chapter，we summarize the main work and give some prospect forthe further research work.