IJPAM: Volume 50, No. 2 (2009)

NONCOMMUTATIVE SOLITONS AND KINKS IN
THE AFFINE TODA MODEL COUPLED TO MATTER

Harold Blas$^1$, Hector L. Carrion$^2$
$^1$Instituto de Física
Universidade Federal de Mato Grosso
Av. Fernando Correa, S/N, Coxipó
Cidade Universitária, Cuiabá - MT, 78060-900, BRAZIL
e-mail: [email protected]
$^2$Instituto de Física
Universidade de São Paulo,
Caixa Postal 68528, São Paulo, 21941-972, BRAZIL
e-mail: [email protected]


Abstract.Some properties of the non-commutative (NC) versions of the generalized sine-Gordon model (NCGSG) and its dual massive Thirring theory are studied. Our method relies on the NC extension of integrable models and the master lagrangian approach to deal with dual theories. The master lagrangian turns out to be the NC version of the so-called affine Toda model coupled to matter related to the group $GL(n)$, in which the Toda field $g \subset GL(n)$ $(n=2, 3)$. Moreover, as a reduction of $GL(3)$ NCGSG one gets a NC version of the remarkable double sine-Gordon model.

Received: August 14, 2008

AMS Subject Classification: 35Q51, 35Q53, 58B25, 58B34

Key Words and Phrases: noncommutative solitons, Toda model coupled to matter, (generalized) sine-Gordon, massive Thirring

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 2