Abstract
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.
| Original language | English |
|---|---|
| Journal | Studies in Applied Mathematics |
| DOIs | |
| Publication status | Accepted/In press - 2018 Jan 1 |
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ASJC Scopus subject areas
- Applied Mathematics
Cite this
The Derivative Yajima-Oikawa System : Bright, Dark Soliton and Breather Solutions. / Chen, Junchao; Feng, Bao Feng; Maruno, Kenichi; Ohta, Yasuhiro.
In: Studies in Applied Mathematics, 01.01.2018.Research output: Contribution to journal › Article
}
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.
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UR - http://www.scopus.com/inward/citedby.url?scp=85046157378&partnerID=8YFLogxK
U2 - 10.1111/sapm.12216
DO - 10.1111/sapm.12216
M3 - Article
JO - Studies in Applied Mathematics
JF - Studies in Applied Mathematics
SN - 0022-2526
ER -