The Explicit Travelling Wave Solutions Of Reaction Diffusion Equations

In this paper,we use the methods of simple integral and the single parameter Lie group in traditional Lie group,to study the integrability of travelling wave solutions equations in several biological models which have practical background respectively.At last,we get the explicit solutions,the first integrals,or the integrability conditions respectively.The four chapters of this paper are as follows:In the first chapter,the background of selecting this question is introduced briefly, at the same time,the involved concepts and theorems in this lecture are given.In the second chapter,we mainly study a biological model,that is,the Keller-Segel model,whose existence and regularity of travelling wave solutions,and finally,get the explicit solutions under some special conditions.In the third chapter,we mainly study the Liouville integrability of Fisher equations of travelling wave solutions. We use methods of the single parameter Lie group to get the first integral and use the algebra curvilinear solutions to get the Liouville integrability conditions.In the forth chapter,we mainly study the generalized Fisher equations of travelling wave solutions and use the methods of the single parameter Lie group to get the first integral at last.