8 research outputs found
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.
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
Reduction of bihamiltonian systems and separation of variables: an example from the Boussinesq hierarchy
We discuss the Boussinesq system with 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
On bi-Hamiltonian deformations of exact pencils of hydrodynamic type
In this paper we are interested in non trivial bi-Hamiltonian deformations of
the Poisson pencil \omega_{\lambda}=\omega_2+\lambda
\omega_1=u\delta'(x-y)+\f{1}{2}u_x\delta(x-y)+\lambda\delta'(x-y).
Deformations are generated by a sequence of vector fields ,
where each is homogenous of degree with respect to a grading
induced by rescaling. Constructing recursively the vector fields one
obtains two types of relations involving their unknown coefficients: one set of
linear relations and an other one which involves quadratic relations. We prove
that the set of linear relations has a geometric meaning: using
Miura-quasitriviality the set of linear relations expresses the tangency of the
vector fields to the symplectic leaves of and this tangency
condition is equivalent to the exactness of the pencil .
Moreover, extending the results of [17], we construct the non trivial
deformations of the Poisson pencil , up to the eighth order
in the deformation parameter, showing therefore that deformations are
unobstructed and that both Poisson structures are polynomial in the derivatives
of up to that order.Comment: 34 pages, revised version. Proof of Theorem 16 completely rewritten
due to an error in the first versio
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