dorsal/arxiv
View SchemaWhitham-Toda Hierarchy in the Laplacian Growth Problem
| Authors | Mark Mineev-Weinstein, Anton Zabrodin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9912012 |
| URL | https://arxiv.org/abs/solv-int/9912012 |
| Journal | J.Nonlin.Math.Phys.8:212-218,2001 |
Abstract
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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"abstract": "The Laplacian growth problem in the limit of zero surface tension is proved\nto be equivalent to finding a particular solution to the dispersionless Toda\nlattice hierarchy. The hierarchical times are harmonic moments of the growing\ndomain. The Laplacian growth equation itself is the quasiclassical version of\nthe string equation that selects the solution to the hierarchy.",
"arxiv_id": "solv-int/9912012",
"authors": [
"Mark Mineev-Weinstein",
"Anton Zabrodin"
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"journal_ref": "J.Nonlin.Math.Phys.8:212-218,2001",
"title": "Whitham-Toda Hierarchy in the Laplacian Growth Problem",
"url": "https://arxiv.org/abs/solv-int/9912012"
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