Matrix resolvent and the discrete KdV hierarchy

DOI10.1007/s00220-020-03770-9zbMath1454.37065arXiv1903.11578OpenAlexW3103269883MaRDI QIDQ779637

Di Yang, B. A. Dubrovin

Publication date: 14 July 2020

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.11578

zbMATH Keywords

tau functionHodge integralsdiscrete KdV hierarchyToda lattice hierarchy

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Lattice dynamics; integrable lattice equations (37K60)

Related Items

Tau-functions for the Ablowitz–Ladik hierarchy: the matrix-resolvent method, On tau-functions for the KdV hierarchy, GUE via Frobenius manifolds. I: From matrix gravity to topological gravity and back, From wave functions to tau-functions for the Volterra lattice hierarchy, On the large genus asymptotics of psi-class intersection numbers, The constrained KP hierarchy and the bigraded Toda hierarchy of \((M, 1)\)-type, Laguerre ensemble: correlators, Hurwitz numbers and Hodge integrals, Grothendieck’s dessins d’enfants in a web of dualities. III

Cites Work

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• Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs
• Hermitian matrix model free energy: Feynman graph technique for all genera
• Quantum field theory techniques in graphical enumeration
• D-particles, matrix integrals and KP hierarchy.
• Generating series for GUE correlators
• On cubic Hodge integrals and random matrices
• The Euler characteristic of the moduli space of curves
• Hodge integrals and invariants of the unknot
• A proof of a conjecture of Mariño-Vafa on Hodge integrals
• Gromov-Witten invariants of the Riemann sphere
• On tau-functions for the Toda lattice hierarchy
• Relating ordinary and fully simple maps via monotone Hurwitz numbers
• On Gromov-Witten invariants of \(\mathbb{P}^1\)
• Correlation functions of the KdV hierarchy and applications to intersection numbers over \(\overline{\mathcal{M}}_{g, n}\)
• Asymptotics for the partition function in two-cut random matrix models
• Hamiltonian Perturbations of Hyperbolic PDEs: from Classification Results to the Properties of Solutions
• On the Toda Lattice. II: Inverse-Scattering Solution
• Simple Lie Algebras and Topological ODEs
• On the gauge theory/geometry correspondence
• Hyperelliptic Prym varieties and integrable systems