Two-dimensional gap solitons in cubic-quintic nonlinear media with PT-symmetric lattices and fractional diffraction

Abstract

Gap solitons in two types of cubic-quintic nonlinear media—the competing focusing-defocusing and the cooperative focusing-focusing types—are studied in this work. We discover two families of two-dimensional solitons in the semi-infinite band gap of a PT-symmetric lattice under the cubic-quintic nonlinearity and fractional diffraction. The existence and stability domains of dipole and tripole solitons are examined for different values of various parameters. Interestingly, the Lévy index does not affect much the value of the phase transformation point in the model, but affects more strongly the stability regions of both types of solitons. The stability domains for these solitons are obtained by the linear stability analysis and are confirmed by direct numerical simulations.