Multi-dark soliton solutions of the two-dimensional multi-component Yajima-Oikawa systems

Junchao Chen, Yong Chen, Bao Feng Feng, Kenichi Maruno

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

We present a general form of multi-dark soliton solutions of two-dimensional (2D) multi-component soliton systems. Multi-dark soliton solutions of the 2D and 1D multi-component Yajima-Oikawa (YO) systems, which are often called the 2D and 1D multi-component long wave-short wave resonance interaction systems, are studied in detail. Taking the 2D coupled YO system with two short wave and one long wave components as an example, we derive the general N-dark-dark soliton solution in both the Gram type and Wronski type determinant forms for the 2D coupled YO system via the KP hierarchy reduction method. By imposing certain constraint conditions, the general N-dark-dark soliton solution of the 1D coupled YO system is further obtained. The dynamics of one dark-dark and two dark-dark solitons are analyzed in detail. In contrast with bright-bright soliton collisions, it is shown that dark -dark soliton collisions are elastic and there is no energy exchange among solitons in different components. Moreover, the dark-dark soliton bound states including the stationary and moving ones are discussed. For the stationary case, the bound states exist up to arbitrary order, whereas, for the moving case, only the two-soliton bound state is possible under the condition that the coefficients of nonlinear terms have opposite signs.

Original languageEnglish
Article number034002
JournalJournal of the Physical Society of Japan
Volume84
Issue number3
DOIs
Publication statusPublished - 2015 Mar 15
Externally publishedYes

Fingerprint

solitary waves
planetary waves
determinants
hierarchies
elastic scattering
energy transfer
collisions
coefficients

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Multi-dark soliton solutions of the two-dimensional multi-component Yajima-Oikawa systems. / Chen, Junchao; Chen, Yong; Feng, Bao Feng; Maruno, Kenichi.

In: Journal of the Physical Society of Japan, Vol. 84, No. 3, 034002, 15.03.2015.

Research output: Contribution to journalArticle

@article{32c00b5953f142a7b63ff05989ebd537,
title = "Multi-dark soliton solutions of the two-dimensional multi-component Yajima-Oikawa systems",
abstract = "We present a general form of multi-dark soliton solutions of two-dimensional (2D) multi-component soliton systems. Multi-dark soliton solutions of the 2D and 1D multi-component Yajima-Oikawa (YO) systems, which are often called the 2D and 1D multi-component long wave-short wave resonance interaction systems, are studied in detail. Taking the 2D coupled YO system with two short wave and one long wave components as an example, we derive the general N-dark-dark soliton solution in both the Gram type and Wronski type determinant forms for the 2D coupled YO system via the KP hierarchy reduction method. By imposing certain constraint conditions, the general N-dark-dark soliton solution of the 1D coupled YO system is further obtained. The dynamics of one dark-dark and two dark-dark solitons are analyzed in detail. In contrast with bright-bright soliton collisions, it is shown that dark -dark soliton collisions are elastic and there is no energy exchange among solitons in different components. Moreover, the dark-dark soliton bound states including the stationary and moving ones are discussed. For the stationary case, the bound states exist up to arbitrary order, whereas, for the moving case, only the two-soliton bound state is possible under the condition that the coefficients of nonlinear terms have opposite signs.",
author = "Junchao Chen and Yong Chen and Feng, {Bao Feng} and Kenichi Maruno",
year = "2015",
month = "3",
day = "15",
doi = "10.7566/JPSJ.84.034002",
language = "English",
volume = "84",
journal = "Journal of the Physical Society of Japan",
issn = "0031-9015",
publisher = "Physical Society of Japan",
number = "3",

}

TY - JOUR

T1 - Multi-dark soliton solutions of the two-dimensional multi-component Yajima-Oikawa systems

AU - Chen, Junchao

AU - Chen, Yong

AU - Feng, Bao Feng

AU - Maruno, Kenichi

PY - 2015/3/15

Y1 - 2015/3/15

N2 - We present a general form of multi-dark soliton solutions of two-dimensional (2D) multi-component soliton systems. Multi-dark soliton solutions of the 2D and 1D multi-component Yajima-Oikawa (YO) systems, which are often called the 2D and 1D multi-component long wave-short wave resonance interaction systems, are studied in detail. Taking the 2D coupled YO system with two short wave and one long wave components as an example, we derive the general N-dark-dark soliton solution in both the Gram type and Wronski type determinant forms for the 2D coupled YO system via the KP hierarchy reduction method. By imposing certain constraint conditions, the general N-dark-dark soliton solution of the 1D coupled YO system is further obtained. The dynamics of one dark-dark and two dark-dark solitons are analyzed in detail. In contrast with bright-bright soliton collisions, it is shown that dark -dark soliton collisions are elastic and there is no energy exchange among solitons in different components. Moreover, the dark-dark soliton bound states including the stationary and moving ones are discussed. For the stationary case, the bound states exist up to arbitrary order, whereas, for the moving case, only the two-soliton bound state is possible under the condition that the coefficients of nonlinear terms have opposite signs.

AB - We present a general form of multi-dark soliton solutions of two-dimensional (2D) multi-component soliton systems. Multi-dark soliton solutions of the 2D and 1D multi-component Yajima-Oikawa (YO) systems, which are often called the 2D and 1D multi-component long wave-short wave resonance interaction systems, are studied in detail. Taking the 2D coupled YO system with two short wave and one long wave components as an example, we derive the general N-dark-dark soliton solution in both the Gram type and Wronski type determinant forms for the 2D coupled YO system via the KP hierarchy reduction method. By imposing certain constraint conditions, the general N-dark-dark soliton solution of the 1D coupled YO system is further obtained. The dynamics of one dark-dark and two dark-dark solitons are analyzed in detail. In contrast with bright-bright soliton collisions, it is shown that dark -dark soliton collisions are elastic and there is no energy exchange among solitons in different components. Moreover, the dark-dark soliton bound states including the stationary and moving ones are discussed. For the stationary case, the bound states exist up to arbitrary order, whereas, for the moving case, only the two-soliton bound state is possible under the condition that the coefficients of nonlinear terms have opposite signs.

UR - http://www.scopus.com/inward/record.url?scp=84924942929&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84924942929&partnerID=8YFLogxK

U2 - 10.7566/JPSJ.84.034002

DO - 10.7566/JPSJ.84.034002

M3 - Article

VL - 84

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 3

M1 - 034002

ER -