Whitham hierarchy in growth problems
نویسندگان
چکیده
منابع مشابه
2 00 4 Whitham hierarchy in growth problems ∗
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 one to distinguish a class of exact solutions to the Laplacian growth problem in the multiply-connected case. These solutions corerespond to finite-dimensional reductions of the Whitham hierarchy re...
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The Laplacian growth problem in the limit of zero surface tension is proved to be equivalent to finding a particular solution to the dispersionless Toda lattice hierarchy. The hierarchical times are harmonic moments of the growing domain. The Laplacian growth equation itself is the quasiclassical version of the string equation that selects the solution to the hierarchy. The Laplacian growth pro...
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The second derivatives of prepotential with respect to Whitham time-variables in the Seiberg-Witten theory are expressed in terms of Riemann theta-functions. These formulas give a direct transcendental generalization of algebraic ones for the Kontsevich matrix model. In particular case they provide an explicit derivation of the renormalization group (RG) equation proposed recently in papers on ...
متن کامل0 40 40 05 v 2 2 9 A pr 2 00 4 Whitham hierarchy in growth problems ∗
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 one to distinguish a class of exact solutions to the Laplacian growth problem in the multiply-connected case. These solutions corerespond to finite-dimensional reductions of the Whitham hierarchy re...
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We have generalized the approach in of Dunajski, Mason and Tod [10] and established a 1-1 correspondence between a solution of the universal Whitham hierarchy [23] and a twistor space. The twistor space consists of a complex surface and a family of complex curves together with a meromorphic 2-form. The solution of the Whitham hierarchy is given by deforming the curve in the surface. By treating...
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ژورنال
عنوان ژورنال: Theoretical and Mathematical Physics
سال: 2005
ISSN: 0040-5779,1573-9333
DOI: 10.1007/s11232-005-0002-4