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

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

Research output: Contribution to journalArticle

19 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
Externally publishedYes

Fingerprint

hodographs
Plane Curve
Integrable Systems
Solitons
Discrete Systems
Soliton Equation
Motion
curves
Discretization
Beam Equation
Short Pulse
Sine-Gordon Equation
solitary waves
Korteweg-de Vries Equation
Analogue
Curve
analogs
pulses

ASJC Scopus subject areas

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

Cite this

Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves. / Feng, Bao Feng; Inoguchi, Jun Ichi; Kajiwara, Kenji; Maruno, Kenichi; Ohta, Yasuhiro.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 44, No. 39, 395201, 30.09.2011.

Research output: Contribution to journalArticle

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