Interactions of vector solitons

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Abstract
In this paper, we study the interaction of two widely separated vector solitons in the nonintegrable coupled nonlinear Schrödinger (NLS) equations. Using a modification of Karpman-Solov’ev perturbation method, we derive dynamical equations for the evolution of both solitons’ internal parameters. We show that these dynamical equations allow fixed points that correspond to stationary two-vector-soliton bound states if these solitons have the same phase in one component (same sign) and π-phase difference in the other component (opposite sign). However, linear stability analysis indicates that these bound states are always unstable due to a phase-related unstable eigenvalue. We also investigate vector-soliton interactions and show that, in contrast to soliton interactions in the single NLS equation, vector solitons repel or attract each other depending not only on their relative phases but also on their initial position separation. Lastly, interaction of an arbitrary number of vector solitons is also studied in brief. All our analytical results are supported by direct numerical simulations.