Oscillations of two-dimensional solitons in harmonic and Bessel optical lattices.

We consider parametric amplification of two-dimensional spatial soliton oscillations in longitudinally modulated harmonic and Bessel lattices in Kerr-type saturable medium. We show that soliton center oscillations along different axes in two-dimensional lattices are coupled, which gives rise to a number of interesting propagation scenarios including periodic damping and excitation of soliton oscillations along perpendicular axes, selective amplification of soliton oscillations along one transverse axis, and enhancement of soliton spiraling.