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Funktsional. Anal. i Prilozhen., 2008, Volume 42, Issue 3, Pages 53–62 (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

Abstract: We consider a class of hydrodynamic type systems that have three independent and $N\ge 2$ 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

DOI: https://doi.org/10.4213/faa2912

Full text: PDF file (191 kB)
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English version:
Functional Analysis and Its Applications, 2008, 42:3, 205–212

Bibliographic databases:

UDC: 517.95
Received: 18.02.2007

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    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. 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
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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