Exact Solutions Of Two Nonlinear Equations With Variable Coefficients

In nonlinear problems,the solution and qualitative analysis of nonlinear evolution equations play an important role.Many breakthroughs have been made in the solution and analysis of constant coefficient nonlinear partial differential equation.At the same time,more and more attention has been paid to the analysis and solution of the nonlinear partial differential equation with variable coefficients.Therefore,it is very important to seek the exact solution of the non-linear partial differential equation with variable coefficients and analyze the properties of the solution.In this paper,we will study the variable coefficient forms of quintic differentiable nonlinear Schr(?)dinger equation and Kd V-CBS equations.First,the relation between the variable coefficient form and the solution of the constant coefficient form is obtained by using the multivariate transformation.Among them,the multivariate transformation used for the Kd V-CBS equation is ternary,while the multivariate transformation used for the quintic differentiable nonlinear Schrodinger equation is complex.Then the range of variable coefficients in the variable coefficient equation are deduced.Next solutions of the two kinds of equations are compared.In addition to rational number form of the Kd V-CBS equation,we obtain solutions of the trigonometric function form,and in addition to the solitary wave solutions of the quintic differentiable nonlinear Schrodinger equation,we obtain periodic wave solutions.In order to study the properties of solutions directly,the numerical software Mathematica is used to draw the three-dimensional images and contour lines of some solutions under different coefficients,which provides a strong theoretical basis for practical application.