Regularization of Hele-Shaw flows, multiscaling expansions and the Painleve I equation

2007/10/19 by Luis Martı́nez Alonso, Luis Martinez Alonso, Alonso, Luis Martinez +3 · 1 citation
Mathematics · Physics and Astronomy · #35Q53 #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Theoretical and Computational Physics #math-ph #math.MP #msc:35Q53 #nlin.SI

paper · pdf · doi:10.48550/arxiv.0710.3731

13 pages, 3 figures

arxiv created 2007/10/19 · openalex publication_date 2007/10/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Critical processes of ideal integrable models of Hele-Shaw flows are considered. A regularization method based on multiscaling expansions of solutions of the KdV and Toda hierarchies characterized by string equations is proposed. Examples are exhibited in which the tritronq'ee solution of the Painleve-I equation turns out to provide the leading term of the regularization

Citations

• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• A common integrable structure in the hermitian matrix model and Hele-Shaw flows

Cited by

• The double scaling limit method in the Toda hierarchy

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