Breather to the Yajima-Oikawa system
Breather to the Yajima-Oikawa system
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发表时间：
2017-12
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通讯作者：
Junchao Chen;Yong Chen;B. Feng;K. Maruno
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作者：
Junchao Chen;Yong Chen;B. Feng;K. Maruno
Yajima-Oikawa（YO）系统描述了在一定条件下长短波之间的共振相互作用。本文通过KP降阶，构造了一维和二维YO系统的呼吸子解。类似于Akhmediev和Kuznetsov-Ma呼吸器解决方案（波数k_i->ik_i），证明了YO系统存在两类呼吸子解，它们的关系为p_{2k-1}->ip_{2k-1}，p_{2k}->-ip_{2k}，q_{2k-1}->iq_{2k-1}和q_{2k}->-iq_{2k}，其中同宿轨道和暗孤子解分别是两种特殊情况。在长波极限条件下，我们得到了包含块波、线流氓波、孤立子及其混合情形的有理解、有理解和有理-exp解。通过考虑进一步的约化，这些解可以约化为一维的YO系统。
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 Schrodinger equation, is shown that the YO system have two kinds ofbreather solutions with the relations p_{2k-1}->ip_{2k-1}, p_{2k}->-ip_{2k}, q_{2k-1}->iq_{2k-1} and q_{2k}->-iq_{2k}, 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.