Singular sectors of the one-layer Benney and dispersionless Toda systems and their interrelations |
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| Authors: | B G Konopelchenko L Martínez Alonso E Medina |
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| Institution: | 1.Dipartimento di Fisica,Universitá del Salento and INFN, Sezione di Lecce,Lecce,Italy;2.Departamento de Física Teórica II,Universidad Complutense,Madrid,Spain;3.Departamento de Matemáticas,Universidad de Cádiz,Puerto Real, Cádiz,Spain |
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| Abstract: | 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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