Solitons of scalar field with induced nonlinearity and their stability

Exact particle-like static, spherically and/or cylindrically symmetric solu tions to the equations of interacting scalar and electromagnetic field syst em have been obtained. We considered FRW and Godel universes as external gr avitational field with spherical and cylindrical symmetry respectively. Bes ide the usual solitons some special regular solutions know as droplets, ant idroplets and hats (confined in finite interval and having trivial value be yond it) have been obtained. It has been shown that in FRW spacetime equati ons with different interaction terms may have stable solutions while within the scope of Godel model only the droplet-like and the hat-like configurat ions may be stable, providing they are located in the region where g(00) > 0.