Whitham hierarchy in growth problems

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

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 distinguishing a class of exact solutions of the Laplacian growth problem in the multiply connected case. These solutions correspond to finite-dimensional reductions of the Whitham hierarchy representable as equations of hydrodynamic type, which are solvable by the generalized hodograph method.

Original languageEnglish
Pages (from-to)166-182
Number of pages17
JournalTheoretical and Mathematical Physics
Volume142
Issue number2
DOIs
Publication statusPublished - Feb 2005
Externally publishedYes

Keywords

  • Laplacian growth
  • Saffman-Taylor problem
  • Schwarz function
  • Whitham equations

Fingerprint

Dive into the research topics of 'Whitham hierarchy in growth problems'. Together they form a unique fingerprint.

Cite this