The Derivative Yajima-Oikawa System: Bright, Dark Soliton and Breather Solutions

Junchao Chen, Bao Feng Feng, Kenichi Maruno, Yasuhiro Ohta

    研究成果: Article

    4 引用 (Scopus)

    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
    ジャーナルStudies in Applied Mathematics
    DOI
    出版物ステータスAccepted/In press - 2018 1 1

    Fingerprint

    Breathers
    Solitons
    Derivatives
    Derivative
    Soliton Solution
    Hirota Bilinear Method
    Elastic collision
    Homoclinic Orbit
    Reduction Method
    Phase Shift
    Asymptotic Analysis
    Determinant
    Nonlinear Equations
    Asymptotic analysis
    Phase shift
    Nonlinear equations
    Orbits
    Interaction

    ASJC Scopus subject areas

    • Applied Mathematics

    これを引用

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

    :: Studies in Applied Mathematics, 01.01.2018.

    研究成果: Article

    @article{3ce7fcda281f4a53b914e950095befc0,
    title = "The Derivative Yajima-Oikawa System: Bright, Dark Soliton and Breather Solutions",
    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 Schr{\"o}dinger 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.",
    author = "Junchao Chen and Feng, {Bao Feng} and Kenichi Maruno and Yasuhiro Ohta",
    year = "2018",
    month = "1",
    day = "1",
    doi = "10.1111/sapm.12216",
    language = "English",
    journal = "Studies in Applied Mathematics",
    issn = "0022-2526",
    publisher = "Wiley-Blackwell",

    }

    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 -