The Hamiltonian structure of soliton equations and deformed scr(W)-algebras

Journal Article · Wed Jan 01 04:00:00 EST 1997 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1997.5621· OSTI ID:503539

Fernandez-Pousa, C R ^[1]; Luis Miramontes, J ^[1]

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1. Departamento de Fisica de Particulas, Facultad de Fisica, Universidad de Santiago, E-15706 Santiago de Compostela (Spain)

The Poisson bracket algebra corresponding to the second Hamiltonian structure of a large class of generalized KdV and mKdV integrable hierarchies is carefully analysed. These algebras are known to have conformal properties and their relation to scr(W)-algebras has been previously investigated in some particular cases. The class of equations that is considered includes practically all the generalizations of the Drinfel{close_quote}d{endash}Sokolov hierarchies constructed in the literature. In particular, it has been recently shown that it includes matrix generalizations of the Gelfand{endash}Dickey and the constrained KP hierarchies. Therefore, our results provide a unified description of the relation between the Hamiltonian structure of soliton equations and scr(W)-algebras, and it comprises almost all the results formerly obtained by other authors. The main result of this paper is an explicit general equation showing that the second Poisson bracket algebra is a deformation of the Dirac bracket algebra corresponding to the scr(W)-algebras obtained through Hamiltonian reduction. {copyright} 1997 Academic Press, Inc.

• OSTI ID: 503539
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 253; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGEBRA
CONFORMAL INVARIANCE
HAMILTONIAN FUNCTION
KORTEWEG-DE VRIES EQUATION
PARTIAL DIFFERENTIAL EQUATIONS
SOLITONS
WAVE EQUATIONS