### 抄録

In this paper, we study the derivative Yajima-Oikawa (YO) system which describes the interaction between long and short waves (SWs). It is shown that the derivative YO system is classified into three types which are similar to the ones of the derivative nonlinear Schrödinger equation. The general N-bright and N-dark soliton solutions in terms of Gram determinants are derived by the combination of the Hirota's bilinear method and the Kadomtsev-Petviashvili hierarchy reduction method. Particularly, it is found that for the dark soliton solution of the SW component, the magnitude of soliton can be larger than the nonzero background for some parameters, which is usually called anti-dark soliton. The asymptotic analysis of two-soliton solutions shows that for both kinds of soliton only elastic collision exists and each soliton results in phase shifts in the long and SWs. In addition, we derive two types of breather solutions from the different reduction, which contain the homoclinic orbit and Kuznetsov-Ma breather solutions as special cases. Moreover, we propose a new (2+1)-dimensional derivative Yajima-Oikawa system and present its soliton and breather solutions.

元の言語 | English |
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ジャーナル | Studies in Applied Mathematics |

DOI | |

出版物ステータス | Accepted/In press - 2018 1 1 |

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### ASJC Scopus subject areas

- Applied Mathematics

### これを引用

*Studies in Applied Mathematics*. https://doi.org/10.1111/sapm.12216

**The Derivative Yajima-Oikawa System : Bright, Dark Soliton and Breather Solutions.** / Chen, Junchao; Feng, Bao Feng; Maruno, Kenichi; Ohta, Yasuhiro.

研究成果: Article

*Studies in Applied Mathematics*. https://doi.org/10.1111/sapm.12216

}

TY - JOUR

T1 - The Derivative Yajima-Oikawa System

T2 - Bright, Dark Soliton and Breather Solutions

AU - Chen, Junchao

AU - Feng, Bao Feng

AU - Maruno, Kenichi

AU - Ohta, Yasuhiro

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this paper, we study the derivative Yajima-Oikawa (YO) system which describes the interaction between long and short waves (SWs). It is shown that the derivative YO system is classified into three types which are similar to the ones of the derivative nonlinear Schrödinger equation. The general N-bright and N-dark soliton solutions in terms of Gram determinants are derived by the combination of the Hirota's bilinear method and the Kadomtsev-Petviashvili hierarchy reduction method. Particularly, it is found that for the dark soliton solution of the SW component, the magnitude of soliton can be larger than the nonzero background for some parameters, which is usually called anti-dark soliton. The asymptotic analysis of two-soliton solutions shows that for both kinds of soliton only elastic collision exists and each soliton results in phase shifts in the long and SWs. In addition, we derive two types of breather solutions from the different reduction, which contain the homoclinic orbit and Kuznetsov-Ma breather solutions as special cases. Moreover, we propose a new (2+1)-dimensional derivative Yajima-Oikawa system and present its soliton and breather solutions.

AB - In this paper, we study the derivative Yajima-Oikawa (YO) system which describes the interaction between long and short waves (SWs). It is shown that the derivative YO system is classified into three types which are similar to the ones of the derivative nonlinear Schrödinger equation. The general N-bright and N-dark soliton solutions in terms of Gram determinants are derived by the combination of the Hirota's bilinear method and the Kadomtsev-Petviashvili hierarchy reduction method. Particularly, it is found that for the dark soliton solution of the SW component, the magnitude of soliton can be larger than the nonzero background for some parameters, which is usually called anti-dark soliton. The asymptotic analysis of two-soliton solutions shows that for both kinds of soliton only elastic collision exists and each soliton results in phase shifts in the long and SWs. In addition, we derive two types of breather solutions from the different reduction, which contain the homoclinic orbit and Kuznetsov-Ma breather solutions as special cases. Moreover, we propose a new (2+1)-dimensional derivative Yajima-Oikawa system and present its soliton and breather solutions.

UR - http://www.scopus.com/inward/record.url?scp=85046157378&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85046157378&partnerID=8YFLogxK

U2 - 10.1111/sapm.12216

DO - 10.1111/sapm.12216

M3 - Article

AN - SCOPUS:85046157378

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

ER -