Lie algebraic structures of (1+1)-dimensional Lax integrable systems

Journal Article · Fri Nov 01 00:00:00 EST 1996 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531742· OSTI ID:392071

Chen, D; Zhang, D ^[1]

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1. Department of Mathematics, Shanghai University, Shanghai 201800, People`s Republic of (China)

An approach of constructing isospectral flows {ital K}{sub {ital l}}, nonisospectral flows {sigma}{sub {ital k}} and their implicit representations of a general Lax integrable system is proposed. By introducing product function matrices, it is shown that the two sets of flows and of related symmetries both constitute infinite-dimensional Lie algebras with respect to the commutator [{center_dot},{center_dot}] given in this paper. Algebraic properties for some well-known integrable systems such as the AKNS system, the generalized Harry Dym system, and the {ital n}-wave interaction system are obtained as particular examples. {copyright} {ital 1996 American Institute of Physics.}

• OSTI ID: 392071
• Journal Information: Journal of Mathematical Physics, Vol. 37, Issue 11; Other Information: PBD: Nov 1996
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 MATHEMATICS
COMPUTERS
INFORMATION SCIENCE
MANAGEMENT
LAW
MISCELLANEOUS
WAVE EQUATIONS
LIE GROUPS
ALGEBRA
SYMMETRY GROUPS
MATRICES
PARTIAL DIFFERENTIAL EQUATIONS
INTEGRABLE SYSTEMS