Tau Functions and their Applications

DOI10.1017/9781108610902zbMath1482.37001OpenAlexW3015682606MaRDI QIDQ3304897

Ferenc Balogh, J. Harnad

Publication date: 4 August 2020

Full work available at URL: https://doi.org/10.1017/9781108610902

zbMATH Keywords

Riemann-Hilbert problemintegrable systemsPlücker relationsClifford algebraGrassmann algebrasKdV hierarchyKP hierarchySchur functionisomonodromic deformationsfermionsBaker functionHirota bilinear equations\(\tau \)-function

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Random matrices (algebraic aspects) (15B52) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Riemann-Hilbert problems in context of PDEs (35Q15) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56) Applications of Clifford algebras to physics, etc. (15A67)

Related Items (18)

Painlevé/CFT correspondence on a torus ⋮ 2D Toda τ functions, weighted Hurwitz numbers and the Cayley graph: Determinant representation and recursion formula ⋮ Tau functions, infinite Grassmannians, and lattice recurrences ⋮ BKP hierarchy, affine coordinates, and a formula for connected bosonic \(n\)-point functions ⋮ Connected (n,m)-point functions of diagonal 2-BKP tau-functions and spin double Hurwitz numbers ⋮ Universal equations for maximal isotropic Grassmannians ⋮ Diagonal tau-functions of 2d Toda lattice hierarchy, connected \((n,m)\)-point functions, and double Hurwitz numbers ⋮ Darboux transformations of the modified BKP hierarchy by fermionic approach ⋮ Differential equations for the KPZ and periodic KPZ fixed points ⋮ Hamiltonian structure of rational isomonodromic deformation systems ⋮ Kac-Schwarz operators of type \(B\), quantum spectral curves, and spin Hurwitz numbers ⋮ Lagrangian Grassmannians, CKP hierarchy and hyperdeterminantal relations ⋮ Universal cusp scaling in random partitions ⋮ Polynomial KP and BKP \(\tau\)-functions and correlators ⋮ Notes about the KP/BKP correspondence ⋮ Isotropic Grassmannians, Plücker and Cartan maps ⋮ Bilinear expansion of Schur functions in Schur Q-functions: A fermionic approach ⋮ Fredholm Pfaffian \(\tau \)-functions for orthogonal isospectral and isomonodromic systems

This page was built for publication: Tau Functions and their Applications