Whitham hierarchy in growth problems
Mathematical Physics
2015-06-26 v2 High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
Abstract
We discuss the recently established equivalence between the Laplacian growth in the limit of zero surface tension and the universal Whitham hierarchy known in soliton theory. This equivalence allows one to distinguish a class of exact solutions to the Laplacian growth problem in the multiply-connected case. These solutions corerespond to finite-dimensional reductions of the Whitham hierarchy representable as equations of hydrodynamic type which are solvable by means of the generalized hodograph method.
Cite
@article{arxiv.math-ph/0404005,
title = {Whitham hierarchy in growth problems},
author = {A. Zabrodin},
journal= {arXiv preprint arXiv:math-ph/0404005},
year = {2015}
}
Comments
20 pages, 4 figures, based on the talk given at the Workshop ``Classical and quantum integrable systems'' (Dubna, January 2004), minor corrections