The multicomponent 2D Toda hierarchy: Discrete flows and string equations

Abstract

The multicomponent 2D Toda hierarchy is analyzed through a factorization problem associated to an infinite-dimensional group. A new set of discrete flows is considered and the corresponding Lax and Zakharov--Shabat equations are characterized. Reductions of block Toeplitz and Hankel bi-infinite matrix types are proposed and studied. Orlov--Schulman operators, string equations and additional symmetries (discrete and continuous) are considered. The continuous-discrete Lax equations are shown to be equivalent to a factorization problem as well as to a set of string equations. A congruence method to derive site independent equations is presented and used to derive equations in the discrete multicomponent KP sector (and also for its modification) of the theory as well as dispersive Whitham equations.

27 pages. In the revised paper we improved the presentation

References in corpus (5)

• The Extended Bigraded Toda hierarchy
• Universal Whitham hierarchy, dispersionless Hirota equations and multi-component KP hierarchy
• Fermionic construction of partition function for multi-matrix models and multi-component TL hierarchy
• Semiclassical expansions in the Toda hierarchy and the hermitian matrix model
• Extended Toda Lattice

Cited by in corpus (14)

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• Orthogonal Laurent polynomials in unit circle, extended CMV ordering and 2D Toda type integrable hierarchies
• Christoffel transformations for matrix orthogonal polynomials in the real line and the non-Abelian 2D Toda lattice hierarchy
• On a classification algorithm of the integrable two-dimensional lattices via Lie-Rinehart algebras
• On the extended multi-component Toda hierarchy
• The multicomponent 2D Toda hierarchy: dispersionless limit
• Classification of a Subclass of Two-Dimensional Lattices via Characteristic Lie Rings
• On the Christoffel--Darboux formula for generalized matrix orthogonal polynomials of multigraded-Hankel type
• Sato theory on the $q$-Toda hierarchy and its extension
• Linear spectral transformations for multivariate orthogonal polynomials and multispectral Toda hierarchies
• Quantum torus algebras and B(C) type Toda systems