Quasi-Noether Systems and Quasi-Lagrangians

Symmetry

V. Rosenhaus¹  Ravi Shankar² 

[1] Department of Mathematics and Statistics, California State University, Chico, CA 95929, USA;Department of Mathematics, University of Washington, Seattle, WA 98195, USA;

关键词: symmetries;    conservation laws;    Noether operator identity;    quasi-Noether systems;    quasi-Lagrangians;   

DOI  :  10.3390/sym11081008

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown