Geodesic
Whitham hierarchy in growth problems
Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 2, pp. 197-217

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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.
Mots-clés : Saffman–Taylor problem
Keywords: Laplacian growth, Whitham equations, Schwarz function. 
A. V. Zabrodin. Whitham hierarchy in growth problems. Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 2, pp. 197-217. http://geodesic.mathdoc.fr/item/TMF_2005_142_2_a1/
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