The Hirota-Satsuma Coupled KdV Equation and a Coupled Ito System Revisited

Abstract

The well-known Hirota-Satsuma coupled KdV equation and a coupled Ito system are reviewed. A new type of soliton solutions to these two systems under constant boundary condition at infinity is found. The so-called generalized Hirota-Satsuma coupled KdV system is also considered. Starting from its bilinear forms, we obtain a Bäcklund transformation and the corresponding nonlinear superposition formulae. As a result, soliton solutions first obtained by Satsuma and Hirota can be rederived. Moreover, rational solutions are also given.