Noncommmutative solitons and kinks in the affine Toda model coupled to matter

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.

6 pages. Talk presented at the Fifth International Conference of Applied Mathematics and Computing (Plovdiv, Bulgaria, August 12 - 18, 2008). Proceedings to appear in special issues of "International Journal of Pure and Applied Mathematics"