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 distinguishing a class of exact solutions of the Laplacian growth problem in the multiply connected case. These solutions correspond to finite-dimensional reductions of the Whitham hierarchy representable as equations of hydrodynamic type, which are solvable by the generalized hodograph method.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol.142, No. 2, pp. 197–217, February, 2005.
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Zabrodin, A.V. Whitham hierarchy in growth problems. Theor Math Phys 142, 166–182 (2005). https://doi.org/10.1007/s11232-005-0045-6
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DOI: https://doi.org/10.1007/s11232-005-0045-6