English

Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

Exactly Solvable and Integrable Systems 2015-05-30 v2 Differential Geometry

Abstract

We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the τ\tau function are presented. B\"acklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation.

Keywords

Cite

@article{arxiv.1108.1328,
  title  = {Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves},
  author = {Jun-ichi Inoguchi and Kenji Kajiwara and Nozomu Matsuura and Yasuhiro Ohta},
  journal= {arXiv preprint arXiv:1108.1328},
  year   = {2015}
}