Breather to the Yajima-Oikawa system

The Yajima-Oikawa (YO) system describes the resonant interaction between long and short waves under certain condition. In this paper, through the KP hierarchy reduction, we construct the breather solutions for the YO system in one- and two-dimensional cases. Similar to Akhmediev and Kuznetsov-Ma breather solutions (the wavenumber k_i → ik_i ) for the nonlinear Schrödinger equation, is shown that the YO system have two kinds of breather solutions with the relations p2_k−1 → ip2_k−1, p2_k → −ip2k, q2_k−1 → iq2_k−1 and q2_k → −iq2k, in which the homoclinic orbit and dark soliton solutions are two special cases respectively. Furthermore, taking the long wave limit, we derive the rational and rational and rational-exp solutions which contain lump, line rogue wave, soliton and their mixed cases. By considering the further reduction, such solutions can be reduced to one-dimensional YO system.