Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves

Bao Feng Feng, Jun Ichi Inoguchi, Kenji Kajiwara, Ken Ichi Maruno, Yasuhiro Ohta

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the WadatiKonnoIchikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sineGordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the EulerLagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations.

Original languageEnglish
Article number395201
JournalJournal of Physics A: Mathematical and Theoretical
Volume44
Issue number39
DOIs
Publication statusPublished - 2011 Sep 30

ASJC Scopus subject areas

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

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