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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 138, Number 1, Pages 55–70
DOI: https://doi.org/10.4213/tmf12 (Mi tmf12) 		 
This article is cited in 37 scientific papers (total in 37 papers)

Classifying Integrable Egoroff Hydrodynamic Chains

M. V. Pavlov

Loughborough University
Full-text PDF (268 kB) Citations (37)
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DOI: https://doi.org/10.4213/tmf12
Abstract: We introduce the notion of Egoroff hydrodynamic chains. We show how they are related to integrable (2+1)-dimensional equations of hydrodynamic type. We classify these equations in the simplest case. We find (2+1)-dimensional equations that are not just generalizations of the already known Khokhlov–Zabolotskaya and Boyer–Finley equations but are much more involved. These equations are parameterized by theta functions and by solutions of the Chazy equations. We obtain analogues of the dispersionless Hirota equations.
Keywords: hydrodynamic chains and lattices, Egoroff integrable systems, dispersionless Hirota equations, tau function.
Received: 15.05.2003
English version:
Theoretical and Mathematical Physics, 2004, Volume 138, Issue 1, Pages 45–58
DOI: https://doi.org/10.1023/B:TAMP.0000010632.20218.62
Bibliographic databases:
Language: Russian
Citation: M. V. Pavlov, “Classifying Integrable Egoroff Hydrodynamic Chains”, TMF, 138:1 (2004), 55–70; Theoret. and Math. Phys., 138:1 (2004), 45–58
Citation in format AMSBIB
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    • This publication is cited in the following 37 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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