Nonlocal Symmetry,Consistent Riccati Expansion Integrability And Interaction Solutions Of (2+1)-dimensional Nonlinear Equations

With the development of nonlinear science,nonlinear equation is one of the most important branch in nonlinear science.Nonlinear equation is the important mathematical model to describe the complex physical phenomenon.Moreover,to solve partial differential equations is the research core in the nonlinear science.Mathematicians and physicists developed a variety of method to solve nonlinear partial equations,inverse scattering method,the CK direct method,the Darboux transformation method.In this manuscript,by employing symbol computation,the residue symmetry,integrability and their interaction solutions of nonlinear equation is detailedly analyzed.This thesis is divided into four section.In the first chapter,the research background of nonlinear equation,integrability and a variety of solution methods are introduced.Moreover,the research progress of this field is discuss,and scientific problem and main thesis is introduced.In the second chapter,the nonlocal symmetry and Lie point symmetry of nonlinear equation.By employing residue symmetry of the truncated Painlel′e expansion method,the nonlocal symmetry of the(2 + 1)-dimensional dispersive long wave equations and(2 + 1)-dimensional konopelchenko dubrovsky equations are obtained.Then,the residue symmetry is known as the lie symmetry of expanded system.In the third chapter,by introducing the consistency of Riccati expansion method to the(2 +1)dimensional dispersive long wave equations,this equation satisfies the consistency of solution Riccati.The solitary wave solution of the(2 + 1)dimensional dispersive long wave equations and the interaction solutions of elliptic periodic wave is obtained by employing consistency conditions.By using numerical simulations,the images of the kink soliton solution and Jacobi elliptic cosine periodic wave solution are provided.The fourth chapter gives the summary and outlook of this dissertaion.