Internal modes of solitons in media with a saturable nonlinearity of the refractive index

The theoretical analysis and calculation of internal modes (eigenmodes of small perturbations) of 1D, 2D, and 3D optical solitons in transparent media with a saturable nonlinearity of the refractive index are performed. Corrections that are nonlinear in the amplitude of perturbations and lead to the radiative damping of internal modes are found. The damping is shown to become weaker with increasing dimensionality of a solition.