Structure-preserving analysis on Gaussian solitary wave solution of logarithmic-KdV equation

Abstract

The existence of the Gaussian solitary wave solution in the logarithmic-KdV equation has aroused considerable interests recently. Focusing on the defects of the reported multi-symplectic analysis on the Gaussian solitary wave solution of the logarithmic-KdV equation and considering the dynamic symmetry breaking of the logarithmic-KdV equation, new approximate multi-symplectic formulations for the logarithmic-KdV equation are deduced and the associated structure-preserving scheme is constructed to simulate the evolution of the Gaussian solitary wave solution. In the structure-preserving simulation process of the Gaussian solitary wave solution, the residuals of three conservation laws are recorded in each step. Comparing with the reported numerical results, it can be found that the Gaussian solitary wave solution can be simulated with tiny numerical errors and three conservation laws are preserved perfectly in the simulation process by the structure-preserving scheme presented in this paper, which implies that the proposed structure-preserving scheme improved the precision as well as the structure-preserving properties of the reported multi-symplectic approach.