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

doi:10.1088/1751-8113/44/39/395201

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

28 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 language	English
Article number	395201
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	44
Issue number	39
DOIs	https://doi.org/10.1088/1751-8113/44/39/395201
Publication status	Published - 2011 Sept 30
Externally published	Yes

ASJC Scopus subject areas

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

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AU - Inoguchi, Jun Ichi

AU - Kajiwara, Kenji

AU - Maruno, Ken Ichi

AU - Ohta, Yasuhiro

PY - 2011/9/30

Y1 - 2011/9/30

N2 - 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.

AB - 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.

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

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