The coupled modified Yajima–Oikawa system: Model derivation and soliton solutions

In this paper, we consider a coupled modified Yajima–Oikawa (YO) system which describes the nonlinear resonant interaction between one long wave (LW) and two short waves (SWs). It is shown that this coupled system can be derived from a three-component modified nonlinear Schrödinger equations through asymptotic reductions. Furthermore, the bright, dark multi-soliton and multi-breather solutions in terms of determinants are obtained respectively by virtue of the bilinear Kadomtsev–Petviashvili-hierarchy reduction technique. The detailed analysis of dynamical properties for one- and two-solitons and breathers is performed, which show the interesting collision properties for the bright and dark solitons. Particularly, differing from the modified YO system with the single SW component, two bright solitons can undergo inelastic collisions and two dark solitons can generate the bound state in the coupled modified YO system. Finally, general bright, dark multi-soliton and multi-breather solutions are presented for the multi-component modified YO system with multi short waves. •A coupled modified Yajima–Oikawa system is derived through asymptotic reductions.•Soliton and breather solutions are obtained via the bilinear KP-hierarchy reduction.•Dynamical properties for one- and two-solitons and breathers are performed.•General soliton solutions and Lax pair are given to a multi-component mYO system.