Interactions between fractional solitons in bimodal fiber cavities

We introduce a system of fractional nonlinear Schroedinger equations (FNLSEs) which model the copropagation of optical waves carried by different wavelengths or mutually orthogonal circular polarizations in fiber-laser cavities with the effective fractional group-velocity dispersion (FGVD), which were recently made available to the experiment. In the FNLSE system, the FGVD terms are represented by the Riesz derivatives, with the respective Levy index (LI). The FNLSEs, which include the nonlinear self-phase-modulation (SPM) nonlinearity, are coupled by the cross-phase modulation (XPM) terms, and separated by a group-velocity (GV) mismatch (rapidity). By means of systematic simulations, we analyze collisions and bound states of solitons in the XPM-coupled system, varying the LI and GV mismatch. Outcomes of collisions between the solitons include rebound, conversion of the colliding single-component solitons into a pair of two-component ones, merger of the solitons into a breather, their mutual passage leading to excitation of intrinsic vibrations, and the elastic interaction. Families of stable two-component soliton bound states are constructed too, featuring a rapidity which is intermediate between those of the two components.
Comment: to be published in Studies in Applied Mathematics (a special issue dedicated to the memory of David J. Kaup)