Deformations of N=2 super-conformal algebra and supersymmetric two-component Camassa-Holm equation

This paper is concerned with a link between central extensions of N=2 superconformal algebra and a supersymmetric two-component generalization of the Camassa--Holm equation. Deformations of superconformal algebra give rise to two compatible bracket structures. One of the bracket structures is derived from the central extension and admits a momentum operator which agrees with the Sobolev norm of a coadjoint orbit element. The momentum operator induces via Lenard relations a chain of conserved hamiltonians of the resulting supersymmetric Camassa-Holm hierarchy.Comment: Latex, 21 pages, version to appear in J. Phys.

Reduction of bihamiltonian systems and separation of variables: an example from the Boussinesq hierarchy

We discuss the Boussinesq system with $t_5$ stationary, within a general framework for the analysis of stationary flows of n-Gel'fand-Dickey hierarchies. We show how a careful use of its bihamiltonian structure can be used to provide a set of separation coordinates for the corresponding Hamilton--Jacobi equations.Comment: 20 pages, LaTeX2e, report to NEEDS in Leeds (1998), to be published in Theor. Math. Phy

Involutive orbits of non-Noether symmetry groups

We consider set of functions on Poisson manifold related by continues one-parameter group of transformations. Class of vector fields that produce involutive families of functions is investigated and relationship between these vector fields and non-Noether symmetries of Hamiltonian dynamical systems is outlined. Theory is illustrated with sample models: modified Boussinesq system and Broer-Kaup system.Comment: LaTeX 2e, 10 pages, no figure

Quantum deformations of associative algebras and integrable systems

Quantum deformations of the structure constants for a class of associative noncommutative algebras are studied. It is shown that these deformations are governed by the quantum central systems which has a geometrical meaning of vanishing Riemann curvature tensor for Christoffel symbols identified with the structure constants. A subclass of isoassociative quantum deformations is described by the oriented associativity equation and, in particular, by the WDVV equation. It is demonstrated that a wider class of weakly (non)associative quantum deformations is connected with the integrable soliton equations too. In particular, such deformations for the three-dimensional and infinite-dimensional algebras are described by the Boussinesq equation and KP hierarchy, respectively.Comment: Numeration of the formulas is correcte

Bihamiltonian reductions and W_n-algebras

Work supported by the Italian M.U.R.S.T. and by the G.N.F.M. of the Italian C.N.R.Consiglio Nazionale delle Ricerche - Biblioteca Centrale -. P.le Aldo Moro, 7, Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

A note on fractional KdV hierarchies

Work supported by the Italian M.U.R.S.T. and by the G.N.F.M. of the Italian C.N.RConsiglio Nazionale delle Ricerche (CNR). Biblioteca Centrale / CNR - Consiglio Nazionale delle RichercheSIGLEITItal