Research On Exact Solutions To Two Kinds Nonlinear Evolution Equations

Many methods have been developed to study the exact solutions of nonlinear equations so far,such as approximate functional separation variable method,compatible Riccati expansion method,invariant subspace method,separation variable method,homogeneous balance method,B?cklund transformation Law and so on.These methods facilitate us to better study the integrability and solution of nonlinear evolution equations,promote the development of nonlinear science,and provide important theoretical basis and scientific methods for studying the solutions of nonlinear equations.In this paper,we use the compatible Riccati expansion(CRE)method to study the interaction solutions of two kinds of nonlinear evolution equations.Firstly,the nonlocal residue symmetry of the(2+1)-dimensional Kadomtsev-Petviashvili equation is discussed.Then the CRE method is used to investigate the compatible Tanh expansion(CTE)solvability of the(2+1)-dimensional KadomSev-PeTviashvili equation under the assumption of negative exponential polynomial.Two different types of interaction solutions for the(2+1)-dimensional KP equation are obtained by choosing different Jacobi elliptic functions.Finally,by selecting the appropriate parameters,the symbolic calculation software maple is used to draw the interaction waveform between the solitary wave and the elliptical periodic wave of the(2+1)-dimensional KP equation.On the other hand,the CRE solvability of a class of(1+1)-dimensional Boussinesq-Burgers equations under the assumption of a negative exponential polynomial is studied.Two types of interaction solutions of Boussinesq-Burgers equation are obtained by choosing different Jacobi elliptic functions,and then the corresponding waveform is drawn by using the symbol calculation software maple by selecting appropriate parameters.Finally,the paper summarizes this article and put forward some thoughts and prospects.