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TMF, 2004, Volume 140, Number 2, Pages 216–229 (Mi tmf91)  

This article is cited in 55 scientific papers (total in 55 papers)

Hydrodynamic Reductions and Solutions of a Universal Hierarchy

L. Martínez Alonsoa, A. B. Shabatb

a Universidad Complutense, Departamento de Fisica Teorica II
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: We investigate the diagonal hydrodynamic reductions of a hierarchy of integrable hydrodynamic chains and analyze their compatibility with previously introduced reductions of differential type.

Keywords: hydrodynamic systems, differential reductions, hodograph solutions

DOI: https://doi.org/10.4213/tmf91

Full text: PDF file (258 kB)
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English version:
Theoretical and Mathematical Physics, 2004, 140:2, 1073–1085

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Received: 17.09.2003

Citation: L. Martínez Alonso, A. B. Shabat, “Hydrodynamic Reductions and Solutions of a Universal Hierarchy”, TMF, 140:2 (2004), 216–229; Theoret. and Math. Phys., 140:2 (2004), 1073–1085

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:
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    5. Ferapontov EV, Khusnutdinova KR, Tsarev SP, “On a class of three-dimensional integrable Lagrangians”, Communications in Mathematical Physics, 261:1 (2006), 225–243  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Henrik Aratyn, Jose Francisco Gomes, Abraham H. Zimerman, “On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa–Holm Equation”, SIGMA, 2 (2006), 070, 12 pp.  mathnet  crossref  mathscinet  zmath
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    30. Morozov O.I. Sergyeyev A., “The Four-Dimensional Martinez Alonso-Shabat Equation: Reductions and Nonlocal Symmetries”, J. Geom. Phys., 85 (2014), 40–45  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
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    45. Hentosh O.E., Prykarpatsky Ya.A., Blackrnore D., Prykarpatski A.K., “Lie-algebraic structure of Lax–Sato integrable heavenly equations and the Lagrange–dAlembert principle”, J. Geom. Phys., 120 (2017), 208–227  crossref  mathscinet  zmath  isi  scopus  scopus
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