Existence, symmetry breaking bifurcation and stability of two-dimensional optical solitons supported by fractional diffraction

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Abstract
We study existence, bifurcation and stability of two-dimensional optical solitons in the framework of fractional nonlinear Schrödinger equation, characterized by its Lévy index, with self-focusing and self-defocusing saturable nonlinearities. We demonstrate that the fractional diffraction system with different Lévy indexes, combined with saturable nonlinearity, supports two-dimensional symmetric, antisymmetric and asymmetric solitons, where the asymmetric solitons emerge by way of symmetry breaking bifurcation. Different scenarios of bifurcations emerge with the change of stability: the branches of asymmetric solitons split off the branches of unstable symmetric solitons with the increase of soliton power and form a supercritical type bifurcation for self-focusing saturable nonlinearity; the branches of asymmetric solitons bifurcates from the branches of unstable antisymmetric solitons for self-defocusing saturable nonlinearity, featuring a convex shape of the bifurcation loops: an antisymmetric soliton loses its stability via a supercritical bifurcation, which is followed by a reverse bifurcation that restores the stability of the symmetric soliton. Furthermore, we found a scheme of restoration or destruction the symmetry of the antisymmetric solitons by controlling the fractional diffraction in the case of self-defocusing saturable nonlinearity.
Funding Information
  • National Natural Science Foundation of China (11805141, 12075210)
  • Applied Basic Research Program of Shanxi Province (201901D211424)
  • Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (2019L0782)
  • “1331 Project” Key Innovative Research Team of Taiyuan Normal University (I0190364)
  • Natural Science Foundation of Zhejiang Province (LR20A050001)

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