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

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 Painle...

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Detalles Bibliográficos
Autores: Martínez Alonso, Luis, Medina Reus, Elena
Tipo de recurso: artículo
Fecha de publicación:2009
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/44793
Acceso en línea:https://hdl.handle.net/20.500.14352/44793
Access Level:acceso abierto
Palabra clave:51-73
Korteweg-devries equation
Small dispersion limit
Integrable hierarchies
Gravity
Dynamics
Strings
Física-Modelos matemáticos
Física matemática
Descripción
Sumario: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.