Second-harmonic generation in the system with fractional diffraction

We construct a family of bright optical solitons composed fundamental-frequency (FF) and second-harmonic (SH) components in the one-dimensional (planar) waveguide with quadratic (second-harmonic-generating) nonlinearity effective fractional diffraction, characterized by Lévy index α, taking values between 2 0.5, which correspond to non-fractional diffraction critical collapse, respectively. The existence domain stability boundary for are delineated space FF-SH mismatch parameter, propagation constant. is tantamount that predicted Vakhitov–Kolokolov criterion, while unstable spontaneously evolve into localized breathers. A sufficiently weak transverse kick applied stable excite small internal vibrations solitons, without setting them motion. stronger makes solitons’ trajectories tilted, simultaneously destabilizing solitons.