Regularization of Hele-Shaw flows, multiscaling expansions and the Painleve I equation
arXiv:0710.3731
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
arXiv comment13 pages, 3 figures
References in corpus (4)
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- Numerical study of a multiscale expansion of KdV and Camassa-Holm equation
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Cited by in corpus (5)
- On the solutions of the second heavenly and Pavlov equations
- The dispersionless 2D Toda equation: dressing, Cauchy problem, longtime behavior, implicit solutions and wave breaking
- Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking
- The double scaling limit method in the Toda hierarchy
- The Cauchy problem for the Pavlov equation