Fundamental and dipole gap solitons and their dynamics in the cubic-quintic fractional nonlinear Schrödinger model with a PT-symmetric lattice

The interplay of two linear controlled terms - fractional diffraction and parity-time (PT ) symmetric lattice - gives rise to unique and interesting linear Bloch gap structures within where the nonlinear localized gap modes may exist. In this study, we explore the formation and dynamics of one-dimensional gap solitons in the cubic-quintic physical model combining the fractional diffraction and PT symmetric lattice. Two classes of gap solitons, which we name the fundamental gap solitons and dipole ones, are constructed and their stability regions within the first finite gap of the associated linear Bloch spectrum are identified by means of linear-stability analysis and direct perturbed numerical simulations. We stress that the gap solitons are always unstable under the condition of PT symmetry breaking (the imaginary part of which is above 0.5). The excitations of the stable two classes of gap solitons are also investigated by using the adiabatic variation of the system's parameters. The results predicted here shed some light on soliton physics in physical systems with combined fractional diffraction and PT symmetric lattice and the competing nonlinearities.