Soliton solutions for a classical field theory withZ(3) symmetry

We construct a matrix scalar nonlinear fieldA by using the Yang-Mills SU(2) component fieldsA µ a in 1+1 dimensions. Under quite general gauge invariance properties ofA and its Lagrangian density, this field can be given a very simple dynamical description in terms of two real scalar fields and a Z(3) discrete symmetry. As a matter of fact, what we present here is the Lagrangian formulation of these two scalar fields, put in interaction by a generic quartic polynomial term. The simplest localized solutions of finite energy and their interactions are thus deduced analytically or numerically. Quite general results concerning theA field and the shape of its potential self-energy are also included.