Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation

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

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a self-adaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well.

    Original languageEnglish
    Article number385202
    JournalJournal of Physics A: Mathematical and Theoretical
    Volume48
    Issue number38
    DOIs
    Publication statusPublished - 2015 Sep 25

    Fingerprint

    Moving Mesh Method
    Adaptive Mesh
    Short Pulse
    Adaptive Method
    Solitons
    mesh
    Discretization
    Computer simulation
    pulses
    determinants
    Determinant
    analogs
    Analogue
    Semidiscretization
    Bilinear form
    Soliton Solution
    solitary waves
    Converge
    Numerical Simulation
    Numerical Results

    Keywords

    • coupled short pulse equation
    • integrable discretization
    • selfadaptive moving mesh method

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics
    • Modelling and Simulation
    • Statistics and Probability

    Cite this

    Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation. / Feng, Bao Feng; Chen, Junchao; Chen, Yong; Maruno, Kenichi; Ohta, Yasuhiro.

    In: Journal of Physics A: Mathematical and Theoretical, Vol. 48, No. 38, 385202, 25.09.2015.

    Research output: Contribution to journalArticle

    @article{06abd4124e2a4e569047d13a92aacd1b,
    title = "Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation",
    abstract = "In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a self-adaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well.",
    keywords = "coupled short pulse equation, integrable discretization, selfadaptive moving mesh method",
    author = "Feng, {Bao Feng} and Junchao Chen and Yong Chen and Kenichi Maruno and Yasuhiro Ohta",
    year = "2015",
    month = "9",
    day = "25",
    doi = "10.1088/1751-8113/48/38/385202",
    language = "English",
    volume = "48",
    journal = "Journal of Physics A: Mathematical and Theoretical",
    issn = "1751-8113",
    publisher = "IOP Publishing Ltd.",
    number = "38",

    }

    TY - JOUR

    T1 - Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation

    AU - Feng, Bao Feng

    AU - Chen, Junchao

    AU - Chen, Yong

    AU - Maruno, Kenichi

    AU - Ohta, Yasuhiro

    PY - 2015/9/25

    Y1 - 2015/9/25

    N2 - In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a self-adaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well.

    AB - In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a self-adaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well.

    KW - coupled short pulse equation

    KW - integrable discretization

    KW - selfadaptive moving mesh method

    UR - http://www.scopus.com/inward/record.url?scp=84941049525&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84941049525&partnerID=8YFLogxK

    U2 - 10.1088/1751-8113/48/38/385202

    DO - 10.1088/1751-8113/48/38/385202

    M3 - Article

    VL - 48

    JO - Journal of Physics A: Mathematical and Theoretical

    JF - Journal of Physics A: Mathematical and Theoretical

    SN - 1751-8113

    IS - 38

    M1 - 385202

    ER -