Nonlinear collective motion

The geometric collective and the Riemann ellipsoidal models are based on the general linear group in three dimensions. The model ansatz that the velocity field is linear is violated unambiguously in some cases, e.g. fissioning isotopes and exotically shaped nuclei. This paper reports a discovery of nonlinear velocity fields on Euclidean space that close under commutation and constructs collective models compatible with such nonlinear velocity fields. Moreover, a family of droplet surfaces is identified that transform among themselves under the nonlinear group action. The integrable nonlinear theory presented here may be applied to many-body collective motion problems in many branches of physics and astronomy. (author)