Skyrme-like solitons with absolute scale in 2+1 dimensions

A family of models involving a complex scalar field in 2+1 dimensions is considered. The most important feature of these models is their quartic kinetic term which makes them simple analogues of systems involving Skyrme-like kinetic terms in dimensions d>2. Their static field configurations in ${\mathit{openR}}_2$ have topological stability. These are studied in some detail, followed by a preliminary formulation of the soliton quantization in 2+1 dimensions. In the Appendix it is demonstrated that the models under discussion are subsystems of the generalization of the Yang-Mills model in higher dimensions.