2005/10/26 by George Bluman, George W. Bluman · 2 citations
Mathematics · Physics and Astronomy · #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.3842/sigma.2005.011
published as SIGMA 1 (2005), 011, 16 pages · Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
openalex publication_date 2005/10/26 · arxiv created 2005/11/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 directly the conservation laws 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.