Perturbation theory for solitons of the Manakov system

We formulate the Kaup-Karpman-Maslov-type perturbation theory for solitons connected with the 3×{}3 matrix spectral problems, using the example of the perturbed Manakov system. The adiabatic approximation and first-order corrections to the soliton shape are considered. The self-orientation effect of the soliton polarization dynamics caused by a cubic perturbation is described. It is also shown that the combined action of linear and cubic perturbations provides existence of a stationary regime for the soliton propagation with the single fixed amplitude and that the corrections to the soliton shape from linear and cubic perturbations partially compensate each other.