Toda lattice hierarchy and Goldstein-Petrich flows for plane curves
Kenji Kajiwara, Saburo Kakei
TL;DR
This paper explores the connection between the Goldstein-Petrich hierarchy and the Toda lattice hierarchy for plane curves, providing representation formulas for both continuous and discretized cases using special tau-functions.
Contribution
It establishes a novel link between two integrable hierarchies and offers explicit formulas for plane curves in terms of tau-functions.
Findings
Relation between Goldstein-Petrich and Toda hierarchies established
Representation formulas for plane curves derived
Discretized plane curves also represented
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 -functions of the Toda lattice hierarchy. A representation formula for discretized plane curves is also discussed.
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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic Geometry and Number Theory · Geometry and complex manifolds