Exact Solutions Of Some Nonlinear Variable Coefficient Partial Differential Equations

At present,the nonlinear evolution equation has been widely used in many fields,among which the study of constant coefficient partial differential equation is more in-depth.However,the equations with constant coefficients are only approximations and ideal values of the real problem.The coefficients of most nonlinear partial differential equations are closely related to time and space,they only combined with these factors together to study more meaningful,also has more research value.Therefore,it is one of the important research topics to study the variable coefficient partial differential equation and explore the form of its solution and the physical meaning behind it.In order to enrich the solution system of partial differential equations with variable coefficients,the validity of the solution is expanded.This paper mainly uses three methods,namely the improved Tanh hyperbolic function expansion method,the second elliptic equation method in the improved Jacobi elliptic function expansion method and the general Riccati equation method to solve the variable coefficient Benjamin-Bona-Mahony-Burgers(BBMB)equation,Kd V-Burgers-Kuramoto(Benny)equation and the generalized variable coefficient Hirota-satsuma equation.The nonlinear equations of ordinary differential equations with variable coefficients are solved by the software Mathematica,a large number of soliton solutions have been solved.Simple analysis of the form of the characteristics of the method,summed up its differences and links,so that in the future work can be better use of this method.The last part is summarized and prospected.First of all,the general work done and the research results obtained,as well as the contribution to the nonlinear development field are summarized.In the prospect part,some unsolved problems arising from soliton solutions of nonlinear partial differential equations(sets)with variable coefficients are explained,as well as the corresponding expectations.