Comparison exact and numerical simulation of the traveling wave solution in nonlinear dynamics

Abstract

The traveling wave solutions of the combined Korteweg de Vries-modified Korteweg de Vries (cKdV-mKdV) equation and a complexly coupled KdV (CcKdV) equation are obtained by using the auto-Backlund Transformation Method (aBTM). To numerically approximate the exact solutions, the Finite Difference Method (FDM) is used. In addition, these exact traveling wave solutions and numerical solutions are compared by illustrating the tables and figures. Via the Fourier-von Neumann stability analysis, the stability of the FDM with the cKdV-mKdV equation is analyzed. The L-2 and L-infinity norm errors are given for the numerical solutions. The 2D and 3D figures of the obtained solutions to these equations are plotted.