Konopelchenko, BorisMartínez Alonso, LuisMedina Reus, Elena2023-06-202023-06-202011-01-310375-960110.1016/j.physleta.2010.12.055https://hdl.handle.net/20.500.14352/44792©2010 Elsevier B.V. All rights reserved. The authors wish to thank the Spanish Ministerio de Educación y Ciencia (research project FIS2008-00200/FIS) for its finantial support. B. K. is thankful to the Departamento de Física Teórica II for the kind hospitalityThe one-cut case of the Hermitian random matrix model in the large N limit is considered. Its singular sector in the space of coupling constants is analyzed from the point of view of the hodograph equations of the underlying dispersionless Toda hierarchy. A deep connection with the singular sector of the hodograph equations of the 1-layer Benney (classical long wave equation) hierarchy is stablished. This property is a consequence of the fact that the hodograph equations for both hierarchies describe the critical points of solutions of Euler- Poisson-Darboux equations.engjournal articlehttp://dx.doi.org/10.1016/j.physleta.2010.12.055http://www.sciencedirect.comhttp://arxiv.org/abs/1005.4773open access51-73Integrable systemsHodograph equationsRandom matrix modelsEuler-Poisson-Darboux equationFísica-Modelos matemáticosFísica matemática