Whitham-Toda hierarchy in the laplacian growth problem

M. Mineev-Weinstein, A. Zabrodin

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)212-218
Number of pages7
JournalJournal of Nonlinear Mathematical Physics
Issue numberSUPPL.
Publication statusPublished - Feb 2001
Externally publishedYes


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