Volume 6, Issue 3, August 1999
Pages: 246 - 254
If we are given a smooth differential operator in the variable x R/2Z, its normal
form, as is well known, is the simplest form obtainable by means of the Diff(S1
action on the space of all such operators. A versal deformation of this operator is a
normal form for some parametric infinitesimal...
Pages: 255 - 262
It is shown that the system of two coupled Korteweg-de Vries equations passes the
Painlevé test for integrability in nine distinct cases of its coefficients. The integrability
of eight cases is verified by direct construction of Lax pairs, whereas for one case it
Pages: 263 - 268
Explicit algebraic relations between the quantum integrals of the elliptic Calogero
Moser quantum problems related to the root systems A2 and B2 are found.
Pages: 269 - 272
If a classical r-matrix r is skewsymmetric, its quantization R can lose the skewsymmetry property. Even when R is skewsymmetric, it may not be unique.
Pages: 273 - 293
In this paper we discuss a universal integrable model, given by a sum of two WessZumino-Witten-Novikov (WZWN) actions, corresponding to two different orbits of
the coadjoint action of a loop group on its dual, and the Polyakov-Weigmann cocycle
describing their interactions. This is an effective action...
Pages: 294 - 313
Analysis of the generalized Weierstrass-Enneper system includes the estimation of
the degree of indeterminancy of the general analytic solution and the discussion of
the boundary value problem. Several different procedures for constructing certain
classes of solutions to this system, including potential,...
Pages: 314 - 331
This paper aims to cast some new light on controlling chaos using the OGY- and
the Zero-Spectral-Radius methods. In deriving those methods we use a generalized
procedure differing from the usual ones. This procedure allows us to conveniently
treat maps to be controlled bringing the orbit to both various...
Pages: 332 - 343
We propose a hamiltonian formulation of the N = 2 supersymmetric KP type hierarchy recently studied by Krivonos and Sorin. We obtain a quadratic hamiltonian
structure which allows for several reductions of the KP type hierarchy. In particular, the third family of N = 2 KdV hierarchies is recovered....
Pages: 344 - 354
A Poisson-Lie group acting by the coadjoint action on the dual of its Lie algebra
induces on it a non-trivial class of quadratic Poisson structures extending the linear
Poisson bracket on the coadjoint orbits.