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Whitham hierarchy in growth problems

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.

preprint2004arXivOpen access
A. Zabrodin
math-phmath.MPnlin.SIhep-th
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A. Zabrodin

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