Laplacian growth and Whitham equations of soliton theory

I. Krichever, M. Mineev-Weinstein, P. Wiegmann, A. Zabrodin

Research output: Contribution to journalArticlepeer-review

57 Citations (Scopus)

Abstract

The Laplacian growth (the Hele-Shaw problem) of multiply-connected domains in the case of zero surface tension is proven to be equivalent to an integrable system of Whitham equations known in soliton theory. The Whitham equations describe slowly modulated periodic solutions of integrable hierarchies of nonlinear differential equations. Through this connection the Laplacian growth is understood as a flow in the moduli space of Riemann surfaces.

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalPhysica D: Nonlinear Phenomena
Volume198
Issue number1-2
DOIs
Publication statusPublished - 1 Nov 2004

Keywords

  • Free boundary problem
  • Hele-Shaw problem
  • Laplacian growth
  • Solution theory
  • Whitham equation

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