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Vladikavkaz. Mat. Zh., 2012, Volume 14, Number 4, Pages 83–94 (Mi vmj440)  

This article is cited in 3 scientific papers (total in 3 papers)

Symmetrical polynomials and conservation laws

A. B. Shabatab

a Landau Institute for Theoretical Physics, Russian Academy of Sciences, Russia, Chernogolovka
b Karachay-Cherkess State University, Russia, Karachaevsk

Abstract: Vector fields with symmetrical polynomials as the first integrals are considered. The connection of these dynamical systems with the theory of multi-phase solutions of the solitonic models of mathematical physics is established.

Key words: Liouville therem, symmetric polynomials, Riemann invariants, solitonic equations.

Full text: PDF file (173 kB)
References: PDF file   HTML file

UDC: 517.928
Received: 30.11.2012

Citation: A. B. Shabat, “Symmetrical polynomials and conservation laws”, Vladikavkaz. Mat. Zh., 14:4 (2012), 83–94

Citation in format AMSBIB
\Bibitem{Sha12}
\by A.~B.~Shabat
\paper Symmetrical polynomials and conservation laws
\jour Vladikavkaz. Mat. Zh.
\yr 2012
\vol 14
\issue 4
\pages 83--94
\mathnet{http://mi.mathnet.ru/vmj440}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. B. Shabat, “Periodic solutions of the Hopf equation”, Theoret. and Math. Phys., 177:2 (2013), 1471–1478  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. 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  isi  scopus
    3. F. Calogero, “Zeros of entire functions and related systems of infinitely many nonlinearly coupled evolution equations”, Theoret. and Math. Phys., 196:2 (2018), 1111–1128  mathnet  crossref  crossref  adsnasa  isi  elib
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