242 research outputs found
Constant curvature solutions of Grassmannian sigma models: (1) Holomorphic solutions
We present a general formula for the Gaussian curvature of curved holomorphic
2-spheres in Grassmannian manifolds G(m, n). We then show how to construct such
solutions with constant curvature. We also make some relevant conjectures for
the admissible constant curvatures in G(m, n) and give some explicit
expressions, in particular, for G(2, 4) and G(2, 5).Comment: 14 page
New solution of the Supersymmetric KdV equation via Hirota methods
We consider the resolution of the supersymmetric KdV equation
with () from the Hirota formalism. For the first time, a
bilinear form of the equation is constructed. We construct
multisoliton solutions and rational similarity solutions.Comment: 7 pages, 9 figures. arXiv admin note: significant text overlap with
arXiv:1104.059
Classification of the quantum deformation of the superalgebra
We present a classification of the possible quantum deformations of the
supergroup and its Lie superalgebra . In each case, the
(super)commutation relations and the Hopf structures are explicitly computed.
For each matrix, one finds two inequivalent coproducts whether one chooses
an unbraided or a braided framework while the corresponding structures are
isomorphic as algebras. In the braided case, one recovers the classical algebra
for suitable limits of the deformation parameters but this is no
longer true in the unbraided case.Comment: 23p LaTeX2e Document - packages amsfonts,subeqn - misprints and
errors corrected, one section adde
Gardner's deformations of the N=2 supersymmetric a=4-KdV equation
We prove that P.Mathieu's Open problem on constructing Gardner's deformation
for the N=2 supersymmetric a=4-Korteweg-de Vries equation has no supersymmetry
invariant solutions, whenever it is assumed that they retract to Gardner's
deformation of the scalar KdV equation under the component reduction. At the
same time, we propose a two-step scheme for the recursive production of the
integrals of motion for the N=2, a=4-SKdV. First, we find a new Gardner's
deformation of the Kaup-Boussinesq equation, which is contained in the bosonic
limit of the super-hierarchy. This yields the recurrence relation between the
Hamiltonians of the limit, whence we determine the bosonic super-Hamiltonians
of the full N=2, a=4-SKdV hierarchy. Our method is applicable towards the
solution of Gardner's deformation problems for other supersymmetric KdV-type
systems.Comment: Extended version of the talks given by A.V.K. at 8th International
conference `Symmetry in Nonlinear Mathematical Physics' (June 20-27, 2009,
Kiev, Ukraine) and 9th International workshop `Supersymmetry and Quantum
Symmetries' (July 29 - August 3, 2009, JINR, Dubna, Russia); 22 page
Squeezed coherent states and the one-dimensional Morse quantum system
The Morse potential one-dimensional quantum system is a realistic model for
studying vibrations of atoms in a diatomic molecule. This system is very close
to the harmonic oscillator one. We thus propose a construction of squeezed
coherent states similar to the one of harmonic oscillator using ladder
operators. Properties of these states are analysed with respect to the
localization in position, minimal Heisenberg uncertainty relation, the
statistical properties and illustrated with examples using the finite number of
states in a well-known diatomic molecule.Comment: 15 pages, 10 figures. Revised section 4, results unchanged.
Correction of formulas 35 and 37. Results unchanged because all variables are
real numbers. arXiv admin note: substantial text overlap with arXiv:1010.327
A convenient criterion under which Z_2-graded operators are Hamiltonian
We formulate a simple and convenient criterion under which skew-adjoint
Z_2-graded total differential operators are Hamiltonian, provided that their
images are closed under commutation in the Lie algebras of evolutionary vector
fields on the infinite jet spaces for vector bundles over smooth manifolds.Comment: J.Phys.Conf.Ser.: Mathematical and Physical Aspects of Symmetry.
Proc. 28th Int. colloq. on group-theoretical methods in Physics (July 26-30,
2010; Newcastle-upon-Tyne, UK), 6 pages (in press
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