The Traveling Wave Solutions Of A Class Of Deformed Boussinesq Coupled Equations

The nature of many phenomena in the real world can be described by nonlinear equations,especially nonlinear differential equations,which play a pivotal role in the rapid development of modern science and human science.Since the 1960s,people have studied the solitary waves.Since the discovery of a large number of integrable systems,physicists and applied mathematicians have been actively involved in the study of exact solutions and qualitative anal-ysis of nonlinear wave equations.The main work of this paper belongs to this research field.We will use the dynamical system branch theory to study the solitary wave solutions of a class of deformed Boussinesq coupled equations.Compared with classical methods such as Jacobian elliptic function expansion,F-expansion,and sub-equilibrium,A prominent advantage of the dynamic sys-tem branching method is that people can use it to obtain the traveling wave solution dynamics phase diagram of the corresponding equation,and then com-bine the parameter classification corresponding to the phase diagram analysis and the classical elliptic function expansion method,etc.And the rich soli-tary wave solutions,trigonometric function solutions,torsional wave solutions,periodic wave solutions and other exact solutions,without some traditional methods require a lot of calculations to get some exact solutions.The main structure of this paper is as follows:The first chapter is about the background of solitary wave research and some classical solutions for trav-eling wave solutions of nonlinear partial differential equations.The second chapter mainly introduces the basic systems of conservative systems,phase di-agrams and elliptic functions.Concepts and results,Chapter 3 uses the method described in Chapter 2 to analyze and solve the traveling wave solutions of the deformed Boussinesq equations.