  We consider parametric amplification of two-dimensional spatial soliton
swinging 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 give rise to a number of
interesting propagation scenarios including periodic damping and excitation of
soliton oscillations along perpendicular axes, selective amplification of
soliton swinging along one of transverse axes and enhancement of soliton
spiraling.
