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

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

13 pages, 3 figures

References in corpus (2)

• Numerical study of a multiscale expansion of KdV and Camassa-Holm equation
• A common integrable structure in the hermitian matrix model and Hele-Shaw flows