Application Of Renormalization Method In The Study Of Progressive Solutions Of Several Kinds Of Nonlinear Equations

Renormalization method is one of the famous methods in physics.In this paper,four kinds of nonlinear equations are studied by renormalization method.That is,mKdv equation,perturbed Kdv equation,Kuikens equation and the large range asymptotic solution of rotating system with boundary conditions in non-Newtonian fluid mechanics.The first chapter is the introduction of this paper,mainly introduces the origin of renormalization methods and the trend of development at home and abroad,and then introduces several kinds of nonlinear equations which are mainly studied in this paper.In the second chapter,the renormalization method is applied to two kinds of boundary free nonlinear equations,namely,mKdv equation and perturbed Kdv equation.The renormalization group method based on Kunihiro envelope theory is used to eliminate the complex terms in the approximate solution,which is convergent at infinity,and their large range asymptotic solutions are obtained.In the third chapter,we mainly introduce the origin and basic idea of homotopy renormalization method,and apply it to study the asymptotic analysis of the rotating system with boundary problem in Kuiken's equation and non-Newtonian fluid mechanics.