Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 198, Issue 1-2, Pages 1-28Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physd.2004.06.003
Keywords
Laplacian growth; Hele-Shaw problem; free boundary problem; solution theory; Whitham equation
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The Laplacian growth (the Hele-Shaw problem) of multiply-connected domains in the case of zero surface tension is proven to be equivalent to an integrable system of Whitham equations known in soliton theory. The Whitham equations describe slowly modulated periodic solutions of integrable hierarchies of nonlinear differential equations. Through this connection the Laplacian,growth is understood as a flow in the moduli space of Riemann surfaces. (C) 2004 Elsevier B.V. All rights reserved.
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