Elliptically oscillating solutions in Abelian-Higgs model and electromagnetic property

The elliptically oscillating solutions in the Abelian Higgs-model are presented and the classical massive-dispersion-relation through the non-linear dynamics is discussed. The generated massive-dispersion-relation including a field value of the scalar field is derived as the consequence of the equation of motions. We discuss the property of the new solutions and its Hamiltonian density. In addition, we calculate the electromagnetic property of the system, in particular, we derive the relation between the field value and the electric field and the electric current-density.Comment: 13 pages, 4 figure