We investigate a model for a real scalar field in bidimensional space-time,
described in terms of a positive semidefinite potential that presents no v
acuum state. The system presents topological solutions of the BPS type. wit
h an energy density that follows a Lorentzian law. These BPS solutions diff
er from the standard tanh-type kink, but they also support bosonic and ferm
ionic zero modes. [S0556-2821(99)05016-X].