The Abdus Salam International Centre for Theoretical Physics Solitons of Scalar Field with Induced Nonlinearity and Their Stability

Exact particle-like static, spherically and/or cylindrically symmetric solutions to the equations of interacting scalar and electromagnetic eld system have been obtained. We considered FRW and G odel universes as external gravitational eld with spherical and cylindrical symmetry respectively. Beside the usual solitons some special regular solutions known as droplets, anti-droplets and hats (con ned in nite interval and having trivial value beyond it) have been obtained. It has been shown that in FRW space-time equations with di erent interaction terms may have stable solutions while within the scope of G odel model only the droplet-like and the hat-like con gurations may be stable, providing that they are located in the region where g > 0. MIRAMARE { TRIESTE September 1999 E-mail: [email protected] Permanent address.