Chiral Dirac-Born-Infeld solitons with SDiff symmetry

We propose a new DBI extension of a Skyrme type model which allows for BPS topological solitons with arbitrary value of the baryon charge. The model is built out of the baryon density squared and in the limit of small fields tends to the BPS Skyrme model. We consider some generalizations to higher dimensions and other K-deformed actions.