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 language | English (US) |
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Article number | 1008 |
Journal | Symmetry |
Volume | 11 |
Issue number | 8 |
DOIs | |
State | Published - 2019 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- General Mathematics
- Physics and Astronomy (miscellaneous)
Keywords
- Conservation laws
- Noether operator identity
- Quasi-Lagrangians
- Quasi-Noether systems
- Symmetries