Singular sectors of the one-layer Benney and dispersionless Toda systems and their interrelations
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2011
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Springer
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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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This work was supported by the Spanish Ministerio de Educación y Ciencia (Research Project No. FIS2008-00200/FIS).