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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 163, Number 1, Pages 3–16
DOI: https://doi.org/10.4213/tmf6483 (Mi tmf6483) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Evolution systems with constraints in the form of zero-divergence conditions

V. V. Zharinov

Steklov Mathematical Institute, RAS, Moscow, Russia
Full-text PDF (470 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf6483
Abstract: We study evolution systems of partial differential equations in the presence of consistent constraints having the form of a system of continuity equations. We show that in addition to possible conservation laws of the standard degree equal to the number of spatial variables, each such system has conservation laws whose degree is one less than this number. We begin by completely describing the conservation laws and symmetries of the system of continuity equations. As an example, we calculate the second-degree conservation laws for the classical system of Maxwell's equations (the number of spatial variables is three here).
Keywords: evolution system, constraint, continuity equation, conservation law, lowest-degree conservation law.
Received: 22.10.2009
English version:
Theoretical and Mathematical Physics, 2010, Volume 163, Issue 1, Pages 401–413
DOI: https://doi.org/10.1007/s11232-010-0031-5
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. V. Zharinov, “Evolution systems with constraints in the form of zero-divergence conditions”, TMF, 163:1 (2010), 3–16; Theoret. and Math. Phys., 163:1 (2010), 401–413
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6483
  • https://doi.org/10.4213/tmf6483
  • https://www.mathnet.ru/eng/tmf/v163/i1/p3
    • This publication is cited in the following 4 articles:
    1. V. V. Zharinov, “Hamiltonian operators with zero-divergence constraints”, Theoret. and Math. Phys., 200:1 (2019), 923–937  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. V. V. Zharinov, “Lie–Poisson structures over differential algebras”, Theoret. and Math. Phys., 192:3 (2017), 1337–1349  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. V. V. Zharinov, “Hamiltonian operators in differential algebras”, Theoret. and Math. Phys., 193:3 (2017), 1725–1736  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. V. V. Zharinov, “Conservation laws, differential identities, and constraints of partial differential equations”, Theoret. and Math. Phys., 185:2 (2015), 1557–1581  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:94
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