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TMF, 2011, Volume 168, Number 1, Pages 125–137 (Mi tmf6668)  

This article is cited in 3 scientific papers (total in 3 papers)

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

B. G. Konopelchenkoa, L. Martínez Alonsob, E. Medinac

a Dipartimento di Fisica, Università del Salento and INFN, Sezione di Lecce, Lecce, Italy
b Departamento de Física Teórica II, Universidad Complutense, Madrid, Spain
c Departamento de Matemáticas, Universidad de Cádiz, Puerto Real, Cádiz, Spain

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 $E(\varepsilon,\varepsilon)$ with the opposite sign of $\varepsilon$.

Keywords: critical point, singular sector, Euler–Poisson–Darboux equation

DOI: https://doi.org/10.4213/tmf6668

Full text: PDF file (461 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 168:1, 963–973

Bibliographic databases:

Document Type: Article

Citation: B. G. Konopelchenko, L. Martínez Alonso, E. Medina, “Singular sectors of the one-layer Benney and dispersionless Toda systems and their interrelations”, TMF, 168:1 (2011), 125–137; Theoret. and Math. Phys., 168:1 (2011), 963–973

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v168/i1/p125

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Konopelchenko B.G., Ortenzi G., “Gradient catastrophe and flutter in vortex filament dynamics”, J. Phys. A: Math. Theor., 44:43 (2011), 432001  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Konopelchenko B.G. Ortenzi G., “Quasi-Classical Approximation in Vortex Filament Dynamics. Integrable Systems, Gradient Catastrophe, and Flutter”, Stud. Appl. Math., 130:2 (2013), 167–199  crossref  mathscinet  zmath  isi  elib  scopus
    3. Konopelchenko B.G., Ortenzi G., “Elliptic Euler-Poisson-Darboux Equation, Critical Points and Integrable Systems”, J. Phys. A-Math. Theor., 46:48 (2013), 485204  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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