Journal
CHAOS SOLITONS & FRACTALS
Volume 173, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2023.113701
Keywords
Second-harmonic generation; Fractional diffraction; Levy index; Quadratic nonlinearity; Bright solitons; Soliton stability; Breathers
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We have constructed a family of bright optical solitons composed of fundamental-frequency (FF) and second-harmonic (SH) components in a one-dimensional waveguide with quadratic nonlinearity and effective fractional diffraction. The stability boundary of the solitons has been determined and is consistent with the Vakhitov-Kolokolov criterion. Unstable solitons evolve into localized breathers. Weak transverse kicks excite small internal vibrations in stable solitons, while stronger kicks tilt the solitons' trajectories and destabilize them.
We construct a family of bright optical solitons composed of fundamental-frequency (FF) and second-harmonic (SH) components in the one-dimensional (planar) waveguide with the quadratic (second-harmonic-generating) nonlinearity and effective fractional diffraction, characterized by the Levy index ������, taking values between 2 and 0.5, which correspond to the non-fractional diffraction and critical collapse, respectively. The existence domain and stability boundary for the solitons are delineated in the space of ������, FF-SH mismatch parameter, and propagation constant. The stability boundary is tantamount to that predicted by the Vakhitov-Kolokolov criterion, while unstable solitons spontaneously evolve into localized breathers. A sufficiently weak transverse kick applied to the stable solitons excite small internal vibrations in the stable solitons, without setting them in motion. A stronger kick makes the solitons' trajectories tilted, simultaneously destabilizing the solitons.
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