Regularization of Hele-Shaw flows, multiscaling expansions and the Painlevé I equation
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2009
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Pergamon-Elsevier Science Ltd
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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.
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©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.