Integrable discretizations of the short pulse equation

Bao Feng Feng, Ken Ichi Maruno, Yasuhiro Ohta

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

In this paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key construction is the bilinear form and determinant structure of solutions of the SP equation. We also give the determinant formulas of N-soliton solutions of the semi-discrete and full-discrete analogues of the SP equations, from which the multi-loop and multi-breather solutions can be generated. In the continuous limit, the full-discrete SP equation converges to the semi-discrete SP equation, and then to the continuous SP equation. Based on the semi-discrete SP equation, an integrable numerical scheme, i.e. a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short pulse equation.

Original languageEnglish
Article number085203
JournalJournal of Physics A: Mathematical and Theoretical
Volume43
Issue number8
DOIs
Publication statusPublished - 2010 Feb 16
Externally publishedYes

ASJC Scopus subject areas

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

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