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

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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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Authors and Affiliations

  1. Dipartimento di Fisica, Universitá del Salento and INFN, Sezione di Lecce, Lecce, Italy

    B. G. Konopelchenko

  2. Departamento de Física Teórica II, Universidad Complutense, Madrid, Spain

    L. Martínez Alonso

  3. Departamento de Matemáticas, Universidad de Cádiz, Puerto Real, Cádiz, Spain

    E. Medina

Authors
  1. B. G. Konopelchenko
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  2. L. Martínez Alonso
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  3. E. Medina
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Corresponding author

Correspondence to B. G. Konopelchenko.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 168, No. 1, pp. 125–137, July, 2011.

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Konopelchenko, B.G., Alonso, L.M. & Medina, E. Singular sectors of the one-layer Benney and dispersionless Toda systems and their interrelations. Theor Math Phys 168, 963–973 (2011). https://doi.org/10.1007/s11232-011-0078-y

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  • DOI: https://doi.org/10.1007/s11232-011-0078-y

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