Polarization dynamics and interactions of solitons in a birefringent optical fiber

Dynamics of vector solitons are studied within the framework of the general model of coupled nonlinear Schr\"odinger equations. The analysis is based upon the perturbation theory for the case when the system is close to the exactly integrable Manakov form. Evolution of the soliton's polarization, coupled by the linear-birefringence terms (which take account of the difference in the group velocity between two linearly polarized modes) to the positional degree of freedom of the soliton, is studied. A four-dimensional dynamical system for the two coupled degrees of freedom integrates to a two-dimensional conservative system. Depending on the value of an arbitrary integration constant, there are four different types of the phase portrait of the latter system. For each value of the polarization angle, there exist two stationary vector solitons, at least one of them being stable. Generic trajectories on the two-dimensional phase plane correspond to oscillations of the polarization coupled to oscillations of the position of the soliton. A generalized model including the polarization-rotating linear coupling is also analyzed. Next, interaction of two slightly overlapping vector solitons is considered, and it is demonstrated that a stable bound state is possible. A stable periodic chain of the slightly overlapping solitons is also found. Finally, radiative decay of a vector soliton is investigated for the case when it has a large component in one subsystem and a small component in another subsystem.