Kac-Moody-Virasoro Symmetries and Related Conservation Laws

Journal Article · Mon Mar 08 04:00:00 EST 2010 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3367027· OSTI ID:21371048

Lou, S Y ^[1]; Jia, M ^[2]; Tang, X Y ^[1]

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1. Department of Physics, Shanghai Jiao Tong University, Shanghai 200240 (China) and Center of Nonlinear Science and Department of Physics, Ningbo University, Ningbo 315211 (China)
2. Department of Physics, Shanghai Jiao Tong University, Shanghai 200240 (China)

In this report, some important facts on the symmetries and conservation laws of high dimensional integrable systems are discussed. It is summarized that almost all the known (2+1)-dimensional integrable models possess the Kac-Moody-Virasoro (KMV) symmetry algebras. One knows that infinitely many partial differential equations may possess a same KMV symmetry algebra. It is found that the KMV symmetry groups can be explicitly obtained by using some direct methods. For some quite general variable coefficient nonlinear systems, their sufficient and necessary condition for the existence of the KMV symmetry algebra is they can be changed to the related known constant coefficient models. Finally, it is found that every one symmetry may be related to infinitely many conservation laws and then infinitely many models may possess a same set of infinitely many conservation laws.

• OSTI ID: 21371048
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 1212; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
EQUATIONS
INTEGRAL CALCULUS
INTEGRAL EQUATIONS
MATHEMATICS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
SYMMETRY
SYMMETRY GROUPS