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Singular sectors of the one-layer Benney and dispersionless Toda systems and their interrelations

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Konopelchenko, Boris and Martínez Alonso, Luis and Medina, E. (2011) Singular sectors of the one-layer Benney and dispersionless Toda systems and their interrelations. Theoretical and mathematical physics, 168 (1). pp. 963-973. ISSN 0040-5779

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Official URL: http://dx.doi.org/10.1007/s11232-011-0078-y


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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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©Springer.
This work was supported by the Spanish Ministerio de Educación y Ciencia (Research Project No. FIS2008-00200/FIS).

Uncontrolled Keywords:Nonlinear schrodinger-equation; Hydrodynamic symmetries; Whitham equations; Deformations; Hierarchy; Curves
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:34173
Deposited On:06 Nov 2015 15:59
Last Modified:10 Dec 2018 15:09

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