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

Autor:	Inoguchi, Jun-ichi, Kajiwara, Kenji, Matsuura, Nozomu, Ohta, Yasuhiro
Rok vydání:	2011
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematics - Differential Geometry 53A04 37K25 37K10 35Q53
Druh dokumentu:	Working Paper
DOI:	10.1088/1751-8113/45/4/045206
Popis:	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 $\tau$ 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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1108.1328 Zobrazit plný text záznamu View this record from Arxiv