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

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 $\tau$ function are presented. Bäcklund 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.

References in corpus (2)

• Motion and Bäcklund Transformations of Discrete Plane Curves
• Discrete curves in CP1 and the Toda lattice

Cited by in corpus (9)

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• Toda lattice hierarchy and Goldstein-Petrich flows for plane curves
• Discrete Local Induction Equation
• Isogonal Deformation of Discrete Plane Curves and Discrete Burgers Hierarchy
• Isoperimetric deformations of curves on the Minkowski plane
• Integrable discretizations of the Dym equation