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TMF, 2017, Volume 192, Number 3, Pages 459–472 (Mi tmf9329)  

This article is cited in 5 scientific papers (total in 5 papers)

Lie–Poisson structures over differential algebras

V. V. Zharinov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: Based on key elements of Olver's approach to partial differential equations for Hamiltonian evolution, we propose an algebraic construction appropriate for Hamiltonian evolutionary systems with constraints.

Keywords: differential algebra, differential bicomplex, Lie–Poisson structure, Hamiltonian map, Hamiltonian evolution system of partial differential equations, constraint.

DOI: https://doi.org/10.4213/tmf9329

Full text: PDF file (469 kB)
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English version:
Theoretical and Mathematical Physics, 2017, 192:3, 1337–1349

Bibliographic databases:

Received: 09.01.2017

Citation: V. V. Zharinov, “Lie–Poisson structures over differential algebras”, TMF, 192:3 (2017), 459–472; Theoret. and Math. Phys., 192:3 (2017), 1337–1349

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. V. V. Zharinov, “Hamiltonian operators in differential algebras”, Theoret. and Math. Phys., 193:3 (2017), 1725–1736  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. K. Gushchin, “A criterion for the existence of $L_p$ boundary values of solutions to an elliptic equation”, Proc. Steklov Inst. Math., 301 (2018), 44–64  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752  mathnet  crossref  crossref  mathscinet  isi
    4. A. K. Gushchin, “On the Existence of $L_2$ Boundary Values of Solutions to an Elliptic Equation”, Proc. Steklov Inst. Math., 306 (2019), 47–65  mathnet  crossref  crossref  mathscinet  isi
    5. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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