34
34

Sep 22, 2013
09/13

by
U. Saleem; M. Hassan

texts

#
eye 34

#
favorite 0

#
comment 0

We investigate one-parameter family of transformation on superfields of super principal chiral model and obtain different zero-curvature representations of the model. The parametric transformation is related to the super Riccati equations and an infinite set of local and non-local conservation laws is derived. A Lax representation of the model is presented which gives rise to a superspace monodromy operator.

Source: http://arxiv.org/abs/hep-th/0501124v1

44
44

Sep 17, 2013
09/13

by
U. Saleem; M. Hassan

texts

#
eye 44

#
favorite 0

#
comment 0

In this paper we present Darboux transformation for the generalized Heisenberg magnet (GHM) model based on general linear Lie group GL(n) and construct multi-soliton solutions in terms of quasideterminants. Further we relate the quasideterminant multi-soliton solutions obtained by the means of Darboux transformation with those of obtained by dressing method. We also discuss the model based on the Lie group SU(n) and obtain explicit soliton solutions of the model based on SU(2).

Source: http://arxiv.org/abs/0912.5030v1

56
56

Jul 20, 2013
07/13

by
Ashok Das; U. Saleem

texts

#
eye 56

#
favorite 0

#
comment 0

We study Darboux transformations for the two boson (TB) hierarchy both in the scalar as well as in the matrix descriptions of the linear equation. While Darboux transformations have been extensively studied for integrable models based on $SL(2,R)$ within the AKNS framework, this model is based on $SL(2,R)\otimes U(1)$. The connection between the scalar and the matrix descriptions in this case implies that the generic Darboux matrix for the TB hierarchy has a different structure from that in the...

Source: http://arxiv.org/abs/1007.3061v1

40
40

Sep 18, 2013
09/13

by
U. Saleem; M. Hassan

texts

#
eye 40

#
favorite 0

#
comment 0

We present a superfield Lax formalism of superspace sigma model based on the target space ${\cal G}/{\cal H}$ and show that a one-parameter family of flat superfield connections exists if the target space ${\cal G}/{\cal H}$ is a symmetric space. The formalism has been related to the existences of an infinite family of local and non-local superfield conserved quantities. Few examples have been given to illustrate the results.

Source: http://arxiv.org/abs/hep-th/0605091v1

55
55

Jul 20, 2013
07/13

by
U. Saleem; M. Hassan

texts

#
eye 55

#
favorite 0

#
comment 0

We present a noncommutative generalization of Lax formalism of U(N) principal chiral model in terms of a one-parameter family of flat connections. The Lax formalism is further used to derive a set of parametric noncommutative B\"{a}cklund transformation and an infinite set of conserved quantities. From the Lax pair, we derive a noncommutative version of the Darboux transformation of the model.

Source: http://arxiv.org/abs/hep-th/0609127v2

57
57

Sep 18, 2013
09/13

by
M. Siddiq; M. Hassan; U. Saleem

texts

#
eye 57

#
favorite 0

#
comment 0

Darboux transformation is constructed for superfields of the super sine-Gordon equation and the superfields of the associated linear problem. The Darboux transformation is shown to be related to the super B\"{a}cklund transformation and is further used to obtain $N$ super soliton solutions.

Source: http://arxiv.org/abs/hep-th/0605094v1

74
74

Sep 18, 2013
09/13

by
U. Saleem; M. Hassan; M. Siddiq

texts

#
eye 74

#
favorite 0

#
comment 0

We construct noncommutative extension of U(N) principal chiral model with Wess-Zumino term and obtain an infinite set of local and non-local conserved quantities for the model using iterative procedure of Brezin {\it et.al} \cite{BIZZ}. We also present the equivalent description as Lax formalism of the model. We expand the fields perturbatively and derive zeroth- and first-order equations of motion, zero-curvature condition, iteration method, Lax formalism, local and non-local conserved...

Source: http://arxiv.org/abs/hep-th/0605092v2

48
48

Sep 18, 2013
09/13

by
U. Saleem; M. Siddiq; M. Hassan

texts

#
eye 48

#
favorite 0

#
comment 0

We give a noncommutative extension of sinh-Gordon equation. We generalize a linear system and Lax representation of the sinh-Gordon equation in noncommutative space. This generalization gives a noncommutative version of the sinh-Gordon equation with extra constraints, which can be expressed as global conserved currents.

Source: http://arxiv.org/abs/hep-th/0605093v2