Constrained Reductions of 2D dispersionless Toda Hierarchy, Hamiltonian Structure and Interface Dynamics
Mathematical Physics
2015-06-26 v4 Statistical Mechanics
High Energy Physics - Theory
Dynamical Systems
math.MP
Fluid 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
Cite
@article{arxiv.math-ph/0312058,
title = {Constrained Reductions of 2D dispersionless Toda Hierarchy, Hamiltonian Structure and Interface Dynamics},
author = {J. Harnad and I. Loutsenko and O. Yermolayeva},
journal= {arXiv preprint arXiv:math-ph/0312058},
year = {2015}
}
Comments
18 pages LaTex, accepted to J.Math.Phys, Significantly updated version of the previous submission