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Funktsional'nyi Analiz i ego Prilozheniya, 2008, Volume 42, Issue 3, Pages 53–62
DOI: https://doi.org/10.4213/faa2912 (Mi faa2912) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On (2+1)-Dimensional Hydrodynamic Type Systems Possessing a Pseudopotential with Movable Singularities

A. V. Odesskiiab, V. V. Sokolova

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b University of Manchester, Department of Mathematics
Full-text PDF (191 kB) Citations (4)
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DOI: https://doi.org/10.4213/faa2912
Abstract: We consider a class of hydrodynamic type systems that have three independent and N⩾2 dependent variables and possess a pseudopotential. It turns out that systems having a pseudopotential with movable singularities can be described by some functional equation. We find all solutions of this equation, which permits constructing interesting examples of integrable systems of hydrodynamic type for arbitrary N.
Keywords: integrable (2+1)-dimensional hydrodynamic type system, pseudopotential with movable singularities.
Received: 18.02.2007
English version:
Functional Analysis and Its Applications, 2008, Volume 42, Issue 3, Pages 205–212
DOI: https://doi.org/10.1007/s10688-008-0029-z
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: A. V. Odesskii, V. V. Sokolov, “On (2+1)-Dimensional Hydrodynamic Type Systems Possessing a Pseudopotential with Movable Singularities”, Funktsional. Anal. i Prilozhen., 42:3 (2008), 53–62; Funct. Anal. Appl., 42:3 (2008), 205–212
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/faa2912
  • https://doi.org/10.4213/faa2912
  • https://www.mathnet.ru/eng/faa/v42/i3/p53
    • This publication is cited in the following 4 articles:
    1. Odesskii A.V., Sokolov V.V., “Non-Homogeneous Systems of Hydrodynamic Type Possessing Lax Representations”, Commun. Math. Phys., 324:1 (2013), 47–62  crossref  mathscinet  zmath  adsnasa  isi
    2. Odesskii A.V., Sokolov V.V., “Integrable pseudopotentials related to generalized hypergeometric functions”, Selecta Math. (N.S.), 16:1 (2010), 145–172  crossref  mathscinet  zmath  isi
    3. A. V. Odesskii, V. V. Sokolov, “Integrable (2+1)-dimensional systems of hydrodynamic type”, Theoret. and Math. Phys., 163:2 (2010), 549–586  mathnet  crossref  crossref  adsnasa  isi  elib
    4. A. V. Odesskii, M. V. Pavlov, V. V. Sokolov, “Classification of integrable Vlasov-type equations”, Theoret. and Math. Phys., 154:2 (2008), 209–219  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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