%0 Journal Article
%A Konopelchenko, Boris
%A Martínez Alonso, Luis
%A Medina, E.
%T Singular sectors of the one-layer Benney and dispersionless Toda systems and their interrelations
%D 2011
%@ 0040-5779
%U https://hdl.handle.net/20.500.14352/44790
%X 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.
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