231 research outputs found
Permutability of Backlund Transformations for N=2 Supersymmetric Sine-Gordon
The permutability of two Backlund transformations is employed to construct a
non linear superposition formula and to generate a class of solutions for the
N=2 super sine-Gordon model.Comment: two references adde
The Conserved Charges and Integrability of the Conformal Affine Toda Models
We construct infinite sets of local conserved charges for the conformal
affine Toda model. The technique involves the abelianization of the
two-dimensional gauge potentials satisfying the zero-curvature form of the
equations of motion. We find two infinite sets of chiral charges and apart from
two lowest spin charges all the remaining ones do not possess chiral densities.
Charges of different chiralities Poisson commute among themselves. We discuss
the algebraic properties of these charges and use the fundamental Poisson
bracket relation to show that the charges conserved in time are in involution.
Connections to other Toda models are established by taking particular limits.Comment: 18 pages, LaTeX, (one appendix and one reference added, small changes
in introduction and conclusions, eqs.(5.14) and (5.19) improved, final
version to appear in Int. J. Modern Phys. A
Grassmanian and Bosonic Thirring Models with Jump Defects
In this paper we discuss the Lax formulation of the Grassmanian and Bosonic
Thirring models in the presence of jump defects. For the Grassmanian case, the
defect is described by B\"acklund transformation which is responsible for
preserving the integrability of the model.
We then propose an extension of the B\"acklund transformation for the Bosonic
Thirring model which is verified by some B\"acklund transitions like
Vacuum-One soliton, One soliton - One soliton, One soliton - Two solitons and
Two solitons - Two solitons. The Lax formulation within the space split by the
defect leads to the integrability of Bosonic Thirring model.Comment: Latex 21 page
Constrained KP Models as Integrable Matrix Hierarchies
We formulate the constrained KP hierarchy (denoted by \cKP) as an
affine matrix integrable hierarchy generalizing the
Drinfeld-Sokolov hierarchy. Using an algebraic approach, including the graded
structure of the generalized Drinfeld-Sokolov hierarchy, we are able to find
several new universal results valid for the \cKP hierarchy. In particular, our
method yields a closed expression for the second bracket obtained through Dirac
reduction of any untwisted affine Kac-Moody current algebra. An explicit
example is given for the case , for which a closed
expression for the general recursion operator is also obtained. We show how
isospectral flows are characterized and grouped according to the semisimple
{\em non-regular} element of and the content of the center of
the kernel of .Comment: LaTeX, 19 pg
Thirring Model with Jump Defect
The purpose of our work is to extend the formulation of classical affine Toda
Models in the presence of jump defects to pure fermionic Thirring model. As a
first attempt we construct the Lagrangian of the Grassmanian Thirring model
with jump defect (of Backlund type) and present its conserved modified momentum
and energy expressions giving a first indication of its integrability.Comment: Poster contribution to the 5th International School on Field Theory
and Gravitation, Cuiaba, MT, Brazil, 20-24 Apr 2009. to be published in PoS
ISFTG(2009
Supersymmetric Construction of W-Algebras from Super Toda and Wznw Theories
A systematic construction of super W-algebras in terms of the WZNW model
based on a super Lie algebra is presented. These are shown to be the symmetry
structure of the super Toda models, which can be obtained from the WZNW theory
by Hamiltonian reduction. A classification, according to the conformal spin
defined by an improved energy-momentum tensor, is dicussed in general terms for
all super Lie algebras whose simple roots are fermionic . A detailed discussion
employing the Dirac bracket structure and an explicit construction of
W-algebras for the cases of , , and are given. The and super conformal algebras are discussed
in the pertinent cases.Comment: 24 page
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