The multicomponent 2D Toda hierarchy: string equations and dispersionless limits.

Abstract:

Motivated by recent applications of multicomponent integrable systems to matrix models, non- intersecting Brownian motions and multiple orthogonal polynomials, we reconsider the multicomponent 2D Toda hierachy from the point of view of a factorization problem in an infinite dimensional Lie group. This formulation allows us to introduce a new set of discrete flows. Two types of dispersionless limits are considered, one leads to the genus 0 universal Whitham hierarchy and the other represents a multicomponent extension of the dispersionless 2D Toda hierarchy. Then, we analyse additional symmetries as well as string equations and their dispersionless limits. These results extend those on multicomponent KP and dispersive Whitham hierarchies presented by Takasaki in the 2005 MISGAM meeting held in Trieste .

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