Solitons, kinks and extended hadron model based on the generalized sine-Gordon theory

The solitons and kinks of the generalized $sl(3, \IC)$ sine-Gordon (GSG)model are explicitly obtained through the hybrid of the Hirota and dressingmethods in which the {\sl tau} functions play an important role. The variousproperties are investigated, such as the potential vacuum structure, thesoliton and kink solutions, and the soliton masses formulae. As a reducedsubmodel we obtain the double sine-Gordon model. Moreover, we provide thealgebraic construction of the $sl(3, \IC)$ affine Toda model coupled to matter(Dirac spinor) (ATM) and through a gauge fixing procedure we obtain theclassical version of the generalized $sl(3, \IC)$ sine-Gordon model (cGSG)which completely decouples from the Dirac spinors. In the spinor sector we areleft with Dirac fields coupled to cGSG fields. Based on the equivalence betweenthe U(1) vector and topological currents it is shown the confinement of thespinors inside the solitons and kinks of the cGSG model providing an extendedhadron model for "quark" confinement.Comment: Latex, 25 pages and 4 figures. Improved version. Accepted for publication in JHE