Bilinear forms and solitonic stability for a variable-coefficient Hirota-Satsuma coupled Korteweg-de Vries system in a liquid

Abstract

In this paper, we investigate a variable-coefficient Hirota-Satsuma coupled Korteweg-de Vries system, which describes the interaction of the long waves with different dispersion relations in a liquid. Via the Hirota method, bilinear forms and N-soliton solutions are derived under certain constraints, where N is a positive integer. On the basis of the one-soliton solutions, we find that not all the one-soliton amplitudes keep unchanged but all the one-soliton velocities are related to the variable coefficients during the propagation. We obtain the profiles of the numerical one soliton with the small perturbation on the variable coefficients of the original system. Under certain constraints, we perturb the initial conditions by 10% and find that the numerical one soliton is stable. We add certain white noise on the initial conditions, and observe that the one component of the numerical one soliton is stable but the other two components of the numerical one soliton v and w are not stable.