Exact Solutions And Localized Structures Of General Breaking Soliton Equation

When coefficients of general breaking soliton equation is selected for some special values, this equation become the physical models of different physical background. In this paper, we constructed exact solutions for typical breaking solition equation, Bogoyavlenskii breaking solition equation, Bogoyavlenskii breaking solition equation with dissipation term and the generalized breaking soliton equation by using the homogeneous balance method and the auxiliary equation method, and analyzed the localized structures.Firstly, we constructed exact solutions of the above mentioned equations and its extended form (variable coefficients form) equations by using the homogeneous balance method.With the homogeneous balance method, we obtained two-soliton solutions that contain arbitrary functions. Through graphic analysis of the obtained solutions,essential law of interaction of the cure solitons are revealed, and some new localized structures are found, and these structures are stable localized structure which are formed by interaction of curve solitons and stick together.Secondly, we constructed infinite sequence exact solutions for extend form equations of above four equations by using the auxiliary equation method. With the help of the second kind of elliptic equation and corresponding Backlund transformation,we obtained infinite sequence exact solutions for extend form equations of the above mentioned equations.Through graphic analysis of the obtained solutions, we obtained arbitrary shape of curve smooth soliton, curve compact soliton solutions and curve peak soliton propagating with variable speed.Furthermore, through analysis of inherent laws of infinite sequence of the equations are given by using Backlund transformation of the second kind,we obtained inherent laws of infinite sequence exact solutions of breaking solition equation.The breaking soliton equation is one of important nonlinear partial differential equations in Applied Mathematics, which describes (2+1)-dimensional interaction of a Riemann wave along the y-axis with a long wave along the x-axis. In this paper, we studied four equations and its extended form equations systematically, the obtained results will play a positive role for in-depth understand nonlinear physical phenomenon by these equations described.