Connections Between Symmetries and Conservation Laws

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2005
• 1. Verfasser: Bluman, G.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2005
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/209349
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Connections Between Symmetries and Conservation Laws / G. Bluman // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 25 назв. — англ.

This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether's theorem and its limitations, we present the Direct Construction Method to show how to find the conservation laws directly for any given system of differential equations. This method yields the multipliers for conservation laws as well as an integral formula for corresponding conserved densities. The action of a symmetry (discrete or continuous) on a conservation law yields conservation laws. Conservation laws yield non-locally related systems that, in turn, can yield nonlocal symmetries and, in addition, be useful for the application of other mathematical methods. From its admitted symmetries or multipliers for conservation laws, one can determine whether or not a given system of differential equations can be linearized by an invertible transformation.