The double scaling limit method in the Toda hierarchy

2008/04/22 by Luis Martı́nez Alonso, L. Martinez Alonso, E. Medina +1 · 10 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Applied mathematics #Computer science #Critical point (mathematics) #Geometry #Hermitian matrix #Hierarchy #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Physics #Property (philosophy) #Pure mathematics #Quantum #Quantum mechanics #Regularization (linguistics) #Scaling #Scaling limit #Semiclassical physics #nlin.SI

paper · pdf · doi:10.1088/1751-8113/41/33/335202

published in Journal of Physics A Mathematical and Theoretical 41(33), 335202 (Institute of Physics) · 20 pages

arxiv created 2008/04/22 · openalex publication_date 2008/07/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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. Key words: Toda hierarchy. Double scaling limit. Hermitian matrix

Citations

• Singularities of the Hele-Shaw Flow and Shock Waves in Dispersive Media
• Numerical study of a multiscale expansion of KdV and Camassa-Holm equation
• Double scaling limit in random matrix models and a nonlinear hierarchy of differential equations
• INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT
• Regularization of Hele-Shaw flows, multiscaling expansions and the Painleve I equation

Cited by

• LargeNexpansions and Painlevé hierarchies in the Hermitian matrix model