Modulation instability analysis and soliton solutions of an integrable coupled nonlinear Schrödinger system

In this paper, an integrable coupled nonlinear Schrödinger system is investigated, which is derived from the integrable Kadomtsev–Petviashvili system, and can be used to describe the stability of soliton in a nonlinear media with weak dispersion. By using the Hirota bilinear method, we derive the exact bilinear formalism and soliton solutions of the system, respectively. Furthermore, we also obtain the linear stability analysis via analyzing the stability condition of the system. Finally, we discuss two kinds of interaction phenomena between solitary wave solutions. It is hoped that our results can be used to enrich the dynamical of the nonlinear Schrödinger system.