A fractional KdV hierarchy

Journal Article · Fri Jun 07 04:00:00 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: NSF; National Science Foundation, Washington, DC (United States)
• OSTI ID: 5196388
• Journal Information: Modern Physics Letters A; (Singapore), Journal Name: Modern Physics Letters A; (Singapore) Vol. 6:17; ISSN 0217-7323; ISSN MPLAE
• Country of Publication: United States
• Language: English

Related Subjects

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