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

Abstract

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.

Authors:
;  [1]
  1. Center for Theoretical Physics, Dept. of Physics and Astronomy, Univ. of Maryland, College Park, MD (US)
Publication Date:
Sponsoring Org.:
National Science Foundation (NSF); National Science Foundation, Washington, DC (United States)
OSTI Identifier:
5594475
Resource Type:
Journal Article
Journal Name:
International Journal of Modern Physics A; (United States)
Additional Journal Information:
Journal Volume: 7:8; Journal ID: ISSN 0217-751X
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; DIFFERENTIAL EQUATIONS; YANG-MILLS THEORY; NONLINEAR PROBLEMS; GAUGE INVARIANCE; KORTEWEG-DE VRIES EQUATION; SPACE-TIME; TWO-DIMENSIONAL CALCULATIONS; EQUATIONS; INVARIANCE PRINCIPLES; PARTIAL DIFFERENTIAL EQUATIONS; 662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)

Citation Formats

Bakas, I, and Depireux, D A. The origin of gauge symmetries in integrable systems of the KdV type. United States: N. p., 1992. Web. doi:10.1142/S0217751X92000764.
Bakas, I, & Depireux, D A. The origin of gauge symmetries in integrable systems of the KdV type. United States. https://doi.org/10.1142/S0217751X92000764
Bakas, I, and Depireux, D A. 1992. "The origin of gauge symmetries in integrable systems of the KdV type". United States. https://doi.org/10.1142/S0217751X92000764.
@article{osti_5594475,
title = {The origin of gauge symmetries in integrable systems of the KdV type},
author = {Bakas, I and Depireux, D A},
abstractNote = {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.},
doi = {10.1142/S0217751X92000764},
url = {https://www.osti.gov/biblio/5594475}, journal = {International Journal of Modern Physics A; (United States)},
issn = {0217-751X},
number = ,
volume = 7:8,
place = {United States},
year = {Mon Mar 30 00:00:00 EST 1992},
month = {Mon Mar 30 00:00:00 EST 1992}
}