Isoperimetric deformations of curves on the Minkowski plane

Hyeongki Park, Jun Ichi Inoguchi, Kenji Kajiwara, Kenichi Maruno, Nozomu Matsuura, Yasuhiro Ohta

Research output: Contribution to journalArticle

Abstract

We formulate an isoperimetric deformation of curves on the Minkowski plane, which is governed by the defocusing modified Korteweg-de Vries (mKdV) equation. Two classes of exact solutions to the defocusing mKdV equation are also presented in terms of the τ functions. By using one of these classes, we construct an explicit formula for the corresponding motion of curves on the Minkowski plane even though those solutions have singular points. Another class gives regular solutions to the defocusing mKdV equation. Some pictures illustrating the typical dynamics of the curves are presented.

Original languageEnglish
JournalInternational Journal of Geometric Methods in Modern Physics
DOIs
Publication statusPublished - 2019 Jan 1

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Keywords

  • defocusing mKdV equation
  • integrable systems
  • Minkowski plane
  • plane curves
  • solitons

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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