Laplacian Growth and Whitham Equations of Soliton Theory

Details Laplacian Growth and Whitham Equations of Soliton Theory Laplacian Growth and Whitham Equations of Soliton Theory

2003-11-03

arxiv.org/abs/nlin/0311005v4

Physica D198 (2004) 1-28

Nonlinear Sciences

Exactly Solvable and Integrable Systems

33 pages, 7 figures, typos corrected, new references added

Scientific paper

10.1016/j.physd.2004.06.003

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.

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