Exact Solutions of Integrable 2D Contour Dynamics

Abstract

A class of exact solutions of the dispersionless Toda hierarchy constrained by a string equation is obtained. These solutions represent deformations of analytic curves with a finite number of nonzero harmonic moments. The corresponding tau-functions are determined and the emergence of cusps is studied.

13 pages, 3 figures

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Cited by in corpus (5)

• On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie
• Genus-zero Whitham hierarchies in conformal-map dynamics
• Conformal Mappings and Dispersionless Toda hierarchy II: General String Equations
• Conformal Mappings and Dispersionless Toda hierarchy
• Hamiltonian motions of plane curves and formation of singularities and bubbles