On Lie symmetries, exact solutions and integrability to the KdV-Sawada-Kotera-Ramani equation

摘要

In this paper, the KdV-Sawada-Kotera-Ramani equation is investigated, which is used to describe the resonances of solitons in one-dimensional space. By using the Lie symmetry analysis method, the vector field and optimal system of the equation are derived, respectively. The optimal system is further used to study the symmetry reductions and exact solutions. Furthermore, the exact analytic solutions of the equation can be obtained by considering the power series theory. Finally, the complete integrability of the equation is systematically presented by using binary Bell's polynomials, which includes the bilinear representation, bilinear Backlund transformation, Lax pair and infinite conservation laws. Based on its bilinear representation, the N-soliton solutions of the equation are also constructed with exact analytic expression.