Fraction-Dimensional Accessible Solitons in a Parity-Time Symmetric Potential

By using the modified Snyder-Mitchell (MSM) model, which can describe the propagation of a paraxial beam in fractional dimensions (FDs), we find the exact "accessible soliton” solutions in the strongly nonlocal nonlinear media with a self-consistent parity-time (PT) symmetric complex potential. The exact solutions are constructed with the help of two special functions: the complex Gegenbauer and the generalized Laguerre polynomials in polar coordinates, parametrized by two nonnegative integer indices - the radial and azimuthal mode numbers (n,m), and the beam modulation depth. By the choice of different soliton parameters, the intensity and angular profiles display symmetric and asymmetric structures. We believe that it is important to explore the MSM model in FDs and PT-symmetric potentials, for a better understanding of nonlinear FD physical phenomena. Different physical systems in which the model might be of relevance are briefly discussed.