The origin of gauge symmetries in integrable systems of the KdV type

Journal Article · Mon Mar 30 04:00:00 EST 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X92000764· OSTI ID:5594475

Bakas, I; Depireux, D A ^[1]

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1. Center for Theoretical Physics, Dept. of Physics and Astronomy, Univ. of Maryland, College Park, MD (US)

Generalized systems of integrable nonlinear differential equations of the KdV type are considered from the point of view of self-dual Yang-Mills theory in space-times with signature. This paper presents a systematic method for embedding the rth flows of the SL(N) KdV hierarchy with N {ge} 2 and r {lt} N in the dimensionally reduced self-dual system using SL(N) as a gauge group. We also find that for r {gt} N the corresponding equations can be described in a similar fashion, provided that (in general) the rank of the gauge group increases accordingly. Certain connections of this formalism with W{sub N} algebras are also discussed. Finally the authors obtain a new class of nonlinear systems in two dimensions by introducing self-dual Ansatze associated with the W{sup (l)} {sub N} algebras of Bershadsky and Polyakov.

• Sponsoring Organization: NSF; National Science Foundation, Washington, DC (United States)
• OSTI ID: 5594475
• Journal Information: International Journal of Modern Physics A; (United States), Journal Name: International Journal of Modern Physics A; (United States) Vol. 7:8; ISSN IMPAE; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
EQUATIONS
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
KORTEWEG-DE VRIES EQUATION
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
SPACE-TIME
TWO-DIMENSIONAL CALCULATIONS
YANG-MILLS THEORY