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

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

2007-10-19

arxiv.org/abs/0710.3731v1

Physics

Mathematical Physics

13 pages, 3 figures

Scientific paper

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

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