Toda lattice hierarchy and Goldstein-Petrich flows for plane curves

Published 26 Oct 2013 in nlin.SI and math.DG | (1310.7080v1)

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.

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