Toda lattice hierarchy and Goldstein-Petrich flows for plane curves

Abstract

A relation between the Goldstein-Petrich hierarchy for plane curves and the Toda lattice hierarchy is investigated. A representation formula for plane curves is given in terms of a special class of $\tau$-functions of the Toda lattice hierarchy. A representation formula for discretized plane curves is also discussed.

16 pages

References in corpus (2)

• Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves
• Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy