N-soliton solutions of Hirota-Satsuma coupled KdV equations with variable coefficients

Abstract

In this paper, we propose a class of generalized variable coefficient Hirota-Satsuma coupled KdV equations, which take into account the inhomogeneity of medium and boundary conditions, and can be used to describe long-wave interactions with different dispersion relationships. The bilinear equations with variable coefficients are obtained by the Hirota bilinear method, 1,2,3, N-soliton solutions are obtained by the perturbation method. In addition, the effects of variable coefficient functions on 1, 2, and 3-soliton solutions are analyzed by numerical simulation, and conclusions are drawn.