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Open AccessArticle

Quasi-Noether Systems and Quasi-Lagrangians

by 1,* and 2
1
Department of Mathematics and Statistics, California State University, Chico, CA 95929, USA
2
Department of Mathematics, University of Washington, Seattle, WA 98195, USA
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(8), 1008; https://doi.org/10.3390/sym11081008
Received: 5 July 2019 / Revised: 1 August 2019 / Accepted: 2 August 2019 / Published: 5 August 2019
(This article belongs to the Special Issue Noether's Theorem and Symmetry)
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. View Full-Text
Keywords: symmetries; conservation laws; Noether operator identity; quasi-Noether systems; quasi-Lagrangians symmetries; conservation laws; Noether operator identity; quasi-Noether systems; quasi-Lagrangians
MDPI and ACS Style

Rosenhaus, V.; Shankar, R. Quasi-Noether Systems and Quasi-Lagrangians. Symmetry 2019, 11, 1008.

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