Quasi-Noether Systems and Quasi-Lagrangians

• Main Authors: V. Rosenhaus, Ravi Shankar
• Format: Article
• Language: English
• Published: MDPI AG 2019-08-01
• Series: Symmetry
• Subjects: symmetries; conservation laws; Noether operator identity; quasi-Noether systems; quasi-Lagrangians
• Online Access: https://www.mdpi.com/2073-8994/11/8/1008

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.