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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 168, Number 1, Pages 125–137
DOI: https://doi.org/10.4213/tmf6668 (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
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DOI: https://doi.org/10.4213/tmf6668
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.
English version:
Theoretical and Mathematical Physics, 2011, Volume 168, Issue 1, Pages 963–973
DOI: https://doi.org/10.1007/s11232-011-0078-y
Bibliographic databases:
Document Type: Article
Language: Russian
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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\paper Singular sectors of the~one-layer Benney and dispersionless Toda systems and their interrelations
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\vol 168
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\pages 125--137
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\crossref{https://doi.org/10.1007/s11232-011-0078-y}
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  • https://doi.org/10.4213/tmf6668
  • https://www.mathnet.ru/eng/tmf/v168/i1/p125
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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