Laplacian Growth and Whitham Equations of Soliton Theory
arXiv:nlin/0311005 · doi:10.1016/j.physd.2004.06.003
Abstract
The Laplacian growth (the Hele-Shaw problem) of multi-connected domains in the case of zero surface tension is proven to be equivalent to an integrable systems 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.
arXiv comment33 pages, 7 figures, typos corrected, new references added
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