Constrained Reductions of 2D dispersionless Toda Hierarchy, Hamiltonian Structure and Interface Dynamics

Abstract

Finite-dimensional reductions of the 2D dispersionless Toda hierarchy, constrained by the ``string equation'' are studied. These include solutions determined by polynomial, rational or logarithmic functions, which are of interest in relation to the ``Laplacian growth'' problem governing interface dynamics. The consistency of such reductions is proved, and the Hamiltonian structure of the reduced dynamics is derived. The Poisson structure of the rationally reduced dispersionless Toda hierarchies is also derived

18 pages LaTex, accepted to J.Math.Phys, Significantly updated version of the previous submission

References in corpus (1)

• Viscous fingering and a shape of an electronic droplet in the Quantum Hall regime

Cited by in corpus (4)

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• On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian Growth
• Non-Laplacian growth, algebraic domains and finite reflection groups
• Solitons and Normal Random Matrices