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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 142, Number 2, Pages 197–217
DOI: https://doi.org/10.4213/tmf1776 (Mi tmf1776) 		 
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
Full-text PDF (352 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf1776
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.
English version:
Theoretical and Mathematical Physics, 2005, Volume 142, Issue 2, Pages 166–182
DOI: https://doi.org/10.1007/s11232-005-0002-4
Bibliographic databases:
Language: Russian
Citation: A. V. Zabrodin, “Whitham hierarchy in growth problems”, TMF, 142:2 (2005), 197–217; Theoret. and Math. Phys., 142:2 (2005), 166–182
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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