Konopelchenko, BorisMartínez Alonso, LuisMedina, E.2023-06-202023-06-202011-070040-577910.1007/s11232-011-0078-yhttps://hdl.handle.net/20.500.14352/44790©Springer. This work was supported by the Spanish Ministerio de Educación y Ciencia (Research Project No. FIS2008-00200/FIS).We completely describe the singular sectors of the one-layer Benney system (classical long-wave equation) and dispersionless Toda system. The associated Euler-Poisson-Darboux equations E(1/2, 1/2) and E(-1/2,-1/2) are the main tool in the analysis. We give a complete list of solutions of the one-layer Benney system depending on two parameters and belonging to the singular sector. We discuss the relation between Euler-Poisson-Darboux equations E(ɛ, ɛ) with the opposite sign of ɛ.engjournal articlehttp://dx.doi.org/10.1007/s11232-011-0078-yhttp://link.springer.comopen access51-73Nonlinear schrodinger-equationHydrodynamic symmetriesWhitham equationsDeformationsHierarchyCurvesFísica-Modelos matemáticosFísica matemática