A class of two dimensional models with extended structure solutions

We study some properties of a class of two-dimensional models which have infinite dimensional groups of symmetry which include both the Euclidean and Minkowskian groups. We show that all solutions of these models are self-dual and correspond to mappings of the 2 dimensional plane into itself which locally preserve the area. When treated as candidates for soliton-like structures we see that the structures are localised. In most cases the energy density of these structures has a power-like tail; in some cases, e.g. the modified sine-Gordon model, the localisation is exponential.