Solitons in curved space

This study presents recent results on the nonlinear evolution of the electromagnetic field in a curved background. A sphere with constant positive, hyperbolic type surface, which has constant negative Gaussian curvature, is being considered. Results show that in curve space, imaginary eigenvalues in the linear stability analysis might not be necessarily interpreted as an instability of the underlying soliton, but can be induced by the exponential expansion in negatively curved space.