ENCAPSULATED-VORTEX SOLUTIONS TO EQUIVARIANT WAVE-EQUATIONS - EXISTENCE

We prove the existence of vector-valued exponentially localized soluti ons to a class of nonlinear elliptic equations with equivariant nonlin earities. The elliptic equations govern the spatial profiles of solita ry wave solutions to nonlinear wave equations with globally regular so lutions. These solitary waves are localized versions of nonlinear Schr odinger vortices. We use constructive methods to show that there are l ocalized solutions with any prescribed number of nodal surfaces.