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This article is cited in 8 scientific papers (total in 8 papers)
Whitham hierarchy in growth problems
A. V. Zabrodinab a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b Institute of biochemical physics of the Russian Academy of Sciences
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.
Keywords:
Saffman–Taylor problem, Laplacian growth, Whitham equations, Schwarz function.
Citation:
A. V. Zabrodin, “Whitham hierarchy in growth problems”, TMF, 142:2 (2005), 197–217; Theoret. and Math. Phys., 142:2 (2005), 166–182
Linking options:
https://www.mathnet.ru/eng/tmf1776https://doi.org/10.4213/tmf1776 https://www.mathnet.ru/eng/tmf/v142/i2/p197
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Abstract page: | 479 | Full-text PDF : | 193 | References: | 48 | First page: | 1 |
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