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

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Martínez Alonso, Luis and Medina Reus, Elena (2009) Regularization of Hele-Shaw flows, multiscaling expansions and the Painlevé I equation. Chaos solitons & Fractals, 41 (3). pp. 1284-1293. ISSN 0960-0779

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Official URL: http://dx.doi.org/10.1016/j.chaos.2008.05.020




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 tritronquee solution of the Painleve-I equation turns out to provide the leading term of the regularization.


Item Type:Article
Additional Information:

©2008 Elsevier Ltd. All rights reserved.
The authors wish to thank the Spanish Ministerio de Educación y Ciencia (research project FIS2005-00319) and the European Science Foundation (MISGAM programme) for their support.

Uncontrolled Keywords:Korteweg-devries equation; Small dispersion limit; Integrable hierarchies; Gravity; Dynamics; Strings
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:34238
Deposited On:17 Nov 2015 18:56
Last Modified:10 Dec 2018 15:09

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