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

Bao Feng Feng, Ken Ichi Maruno, Yasuhiro Ohta

Research output: Contribution to journalArticlepeer-review

9 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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