Formula omitted]-soliton solutions and long-time asymptotic analysis for a generalized complex Hirota–Satsuma coupled KdV equation

Abstract

A generalized Hirota–Satsuma coupled KdV equation, which can describe the interactions of two long waves with different dispersion relations, is studied in this paper. Using the Hirota direct method, its bilinear form is firstly obtained, and secondly its N-soliton solutions are found. Finally, the collisions between two solitons are proved to be elastic via performing the asymptotic analysis. Some graphs are given to illustrate that the two-soliton collisions do not change any physical quantities except small phase shifts.