The double scaling limit method in the Toda hierarchy

Abstract

Critical points of semiclassical expansions of solutions to the dispersionful Toda hierarchy are considered and a double scaling limit method of regularization is formulated. The analogues of the critical points characterized by the strong conditions in the Hermitian matrix model are analyzed and the property of doubling of equations is proved. A wide family of sets of critical points is introduced and the corresponding double scaling limit expansions are discussed.

20 pages

References in corpus (5)

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• Numerical study of a multiscale expansion of KdV and Camassa-Holm equation
• Singular limit of Hele-Shaw flow and dispersive regularization of shock waves
• Semiclassical expansions in the Toda hierarchy and the hermitian matrix model
• Regularization of Hele-Shaw flows, multiscaling expansions and the Painleve I equation