A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue

Bao Feng Feng, Kenichi Maruno, Yasuhiro Ohta

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    In the present paper, we propose a two-component generalization of the reduced Ostrovsky (Vakhnenko) equation, whose differential form can be viewed as the short-wave limit of a two-component Degasperis-Procesi (DP) equation. They are integrable due to the existence of Lax pairs. Moreover, we have shown that the two-component reduced Ostrovsky equation can be reduced from an extended BKP hierarchy with negative flow through a pseudo 3-reduction and a hodograph (reciprocal) transform. As a by-product, its bilinear form and N-soliton solution in terms of pfaffians are presented. One- and two-soliton solutions are provided and analyzed. In the second part of the paper, we start with a modified BKP hierarchy, which is a Bcklund transformation of the above extended BKP hierarchy, an integrable semi-discrete analogue of the two-component reduced Ostrovsky equation is constructed by defining an appropriate discrete hodograph transform and dependent variable transformations. In particular, the backward difference form of above semi-discrete two-component reduced Ostrovsky equation gives rise to the integrable semi-discretization of the short wave limit of a two-component DP equation. Their N-soliton solutions in terms of pffafians are also provided.

    Original languageEnglish
    Article number055201
    JournalJournal of Physics A: Mathematical and Theoretical
    Volume50
    Issue number5
    DOIs
    Publication statusPublished - 2017 Jan 4

    Keywords

    • BKP and modified BKP hierarchy
    • hodograph and discrete hodograph transform
    • integrable discretization
    • pseudo 3-reduction
    • short wave model of two-component Degasperis Procesi (DP) equation
    • two-component reduced Ostrovsky equation

    ASJC Scopus subject areas

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

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