Quasi-noether systems and quasi-Lagrangians

V. Rosenhaus, Ravi Shankar

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Abstract

We study differential systems for which it is possible to establish a correspondence between symmetries and conservation laws based on Noether identity: quasi-Noether systems. We analyze Noether identity and show that it leads to the same conservation laws as Lagrange (Green-Lagrange) identity. We discuss quasi-Noether systems, and some of their properties, and generate classes of quasi-Noether differential equations of the second order. We next introduce a more general version of quasi-Lagrangians which allows us to extend Noether theorem. Here, variational symmetries are only sub-symmetries, not true symmetries. We finally introduce the critical point condition for evolution equations with a conserved integral, demonstrate examples of its compatibility, and compare the invariant submanifolds of quasi-Lagrangian systems with those of Hamiltonian systems.

Original languageEnglish (US)
Article number1008
JournalSymmetry
Volume11
Issue number8
DOIs
StatePublished - 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • Mathematics(all)
  • Physics and Astronomy (miscellaneous)

Keywords

  • Conservation laws
  • Noether operator identity
  • Quasi-Lagrangians
  • Quasi-Noether systems
  • Symmetries

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