Dynamical Poincaré Symmetry Realized by Field-Dependent Diffeomorphisms

We present several Galileo invariant Lagrangians, which are invariant against Poincaré transformations defined in one higher (spatial) dimension. Thus these models, which arise in a variety of physical situations, provide a representation for a dynamical (hidden) Poincaré symmetry. The action of this symmetry transformation on the dynamical variables is nonlinear, and in one case involves a peculiar field-dependent diffeomorphism. Some of our models are completely integrable, and we exhibit explicit solutions.