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

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Cited by in corpus (6)

• Quasi-classical approximation in vortex filament dynamics. Integrable systems, gradient catastrophe and flutter
• Partition functions and the continuum limit in Penner matrix models
• On the singular sector of the Hermitian random matrix model in the large N limit
• Singular sectors of the 1-layer Benney and dToda systems and their interrelations
• Gradient catastrophe and flutter in vortex filament dynamics
• Large N expansions and Painlevé hierarchies in the Hermitian matrix model