The multicomponent 2D Toda hierarchy: dispersionless limit

Abstract

The factorization problem of the multi-component 2D Toda hierarchy is used to analyze the dispersionless limit of this hierarchy. A dispersive version of the Whitham hierarchy defined in terms of scalar Lax and Orlov--Schulman operators is introduced and the corresponding additional symmetries and string equations are discussed. Then, it is shown how KP and Toda pictures of the dispersionless Whitham hierarchy emerge in the dispersionless limit. Moreover, the additional symmetries and string equations for the dispersive Whitham hierarchy are studied in this limit.

Revised version with an overall improved presentation

References in corpus (4)

• Large n limit of Gaussian random matrices with external source, Part III: Double scaling limit
• Universal Whitham hierarchy, dispersionless Hirota equations and multi-component KP hierarchy
• The multicomponent 2D Toda hierarchy: Discrete flows and string equations
• Dyson's non-intersecting Brownian motions with a few outliers

Cited by in corpus (11)

• Multiple orthogonal polynomials of mixed type: Gauss-Borel factorization and the multi-component 2D Toda hierarchy
• The extended $Z_N$-Toda hierarchy
• Multivariate orthogonal polynomial and integrable systems
• Christoffel transformations for matrix orthogonal polynomials in the real line and the non-Abelian 2D Toda lattice hierarchy
• On the extended multi-component Toda hierarchy
• Darboux transformations for multivariate orthogonal polynomials
• On the Christoffel--Darboux formula for generalized matrix orthogonal polynomials of multigraded-Hankel type
• Sato theory on the $q$-Toda hierarchy and its extension
• Transformation theory and Christoffel formulas for matrix biorthogonal polynomials on the real line
• Linear spectral transformations for multivariate orthogonal polynomials and multispectral Toda hierarchies
• Infinite-Dimensional Frobenius Manifolds for 2+1 Integrable Systems