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

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    7 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

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    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

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