INTERNAL VIBRATIONS OF A VECTOR SOLITON IN THE COUPLED NONLINEAR SCHRODINGER-EQUATIONS

Static and dynamic properties of a two-component soliton are studied v ia the variational approximation (VA), consideration of the radiation spectrum, and direct numerical simulations. The VA, based on a Gaussia n Ansatz, proves to be (as compared to the direct simulations) fairly accurate in some respects and inaccurate in others-in particular, the predictions for the widths of the stationary states are about a sixth part greater than the actual widths. We formulate an empirically modif ied version of the variational approximation: at the end of the analys is, the Gaussian is replaced by sech with properly rescaled widths. Th is hybrid VA yields extremely accurate predictions for the stationary states. The error in the width prediction is less than or similar to 1 %, and simulations demonstrate minuscule radiation losses. The VA mode l predicts three eigenmodes of the soliton's internal vibrations, all of which are observed numerically. Oscillation of the separation betwe en the two components is found to be the most persistent mode, and in- phase oscillation of the two widths is the next most persistent one; i n contrast, the out-of-phase width oscillations are unstable, quickly rearranging themselves into the stable in-phase mode. These features a re easily explained by comparing the corresponding vibrational eigenfr equencies to the spectral gaps which isolate oscillations localized at the soliton from delocalized radiation modes. For vector solitons wit h energy nearly equally divided between the components, the analysis r eveals a remarkable feature: saturation of the separation oscillations , with the radiative decay virtually ceasing at a finite level of the mode's amplitude. The relatively stable in-phase width-oscillation mod e decays indefinitely, but according to a very slow power law rather t han exponentially. Lastly, for large-amplitude vibrations, the VA mode ls predict dynamical chaos, but, due to the quick decay of the large o scillations, direct simulations show no chaos.