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The multicomponent 2D Toda hierarchy: dispersionless limit

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Mañas Baena, Manuel and Martínez Alonso, Luis (2009) The multicomponent 2D Toda hierarchy: dispersionless limit. Inverse problems, 25 (11). ISSN 0266-5611

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Official URL: http://dx.doi.org/10.1088/0266-5611/25/11/115020




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.


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©IOP Publishing.
The authors wish to thank the Spanish Ministerio de Ciencia e Innovaciòn, research project FIS2008- 00200, and acknowledge the support received from the European Science Foundation (ESF) and the activity entitled Methods of Integrable Systems, Geometry, Applied Mathematics (MISGAM). MM wish to thank Prof. van Moerbeke and Prof. Dubrovin for their warm hospitality, acknowledge economical support from MISGAM and SISSA and reckons different conversations with P. van Moerbeke, T. Grava, G. Carlet and M. Caffasso. MM also acknowledges to Prof. Liu for his invitation to visit the China Mining and Technology University at Beijing.

Uncontrolled Keywords:Nonintersecting brownian motions; Kadomtsev-petviashvili equation; Multiple orthogonal polynomials; Universal whitham hierarchy; Gaussian random matrices; Riemann-hilbert problem; Large-n limit; Kp hierarchy; Additional symmetries; Biorthogonal polynomials
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:31555
Deposited On:20 Jul 2015 10:57
Last Modified:10 Dec 2018 15:09

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