A fractional KdV hierarchy

Journal Article · Fri Jun 07 00:00:00 EDT 1991 · Modern Physics Letters A; (Singapore)

DOI:https://doi.org/10.1142/S0217732391001688· OSTI ID:5196388

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)

In this paper, the authors construct a new system of integrable nonlinear differential equations associated with the operator algebra W{sup (2)}{sub 3} of Polyakov. Its members are fractional generalizations of KdV type flows corresponding to an alternative set of constraints on the 2-dim. SL(3) gauge connections. The authors obtain the first non-trivial examples by dimensional reduction from self-dual Yang-Mills and then generate recursively the entire hierarchy and its conserved quantities using a bi-Hamiltonian structure. Certain relations with the Boussinesq equation are also discussed together with possible generalizations of the formalism to SL(N) gauge groups and W{sup l}{sub N} operator algebras with arbitrary N and l.

• Sponsoring Organization: National Science Foundation (NSF); National Science Foundation, Washington, DC (United States)
• OSTI ID: 5196388
• Journal Information: Modern Physics Letters A; (Singapore), Vol. 6:17; ISSN 0217-7323
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
SYMMETRY
DIFFERENTIAL EQUATIONS
YANG-MILLS THEORY
COMPACTIFICATION
CONSTRAINTS
GAUGE INVARIANCE
HAMILTONIANS
NONLINEAR PROBLEMS
SL GROUPS
TWO-DIMENSIONAL CALCULATIONS
EQUATIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL OPERATORS
QUANTUM OPERATORS
SYMMETRY GROUPS
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)
661100 - Classical & Quantum Mechanics- (1992-)