Whitham-Toda Hierarchy in the Laplacian Growth Problem

Details Whitham-Toda Hierarchy in the Laplacian Growth Problem Whitham-Toda Hierarchy in the Laplacian Growth Problem

1999-12-18

arxiv.org/abs/solv-int/9912012v1

J.Nonlin.Math.Phys.8:212-218,2001

Physics

Condensed Matter

Statistical Mechanics

7 pages, no figures, Talk given at the Workshop NEEDS 99 (Crete, Greece, June 1999)

Scientific paper

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.

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