Mañas Baena, Manuel EnriqueMartínez Alonso, Luis2023-06-202023-06-202009-110266-561110.1088/0266-5611/25/11/115020https://hdl.handle.net/20.500.14352/44700©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.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.engjournal articlehttp://dx.doi.org/10.1088/0266-5611/25/11/115020http://iopscience.iop.orghttp://arxiv.org/abs/0810.2427open access51-73Nonintersecting brownian motionsKadomtsev-petviashvili equationMultiple orthogonal polynomialsUniversal whitham hierarchyGaussian random matricesRiemann-hilbert problemLarge-n limitKp hierarchyAdditional symmetriesBiorthogonal polynomialsFísica-Modelos matemáticosFísica matemática