Localized Modes in Nonlinear Fractional Systems with Deep Lattices. Issue 4 (25th January 2022) - Liu, Xiuye; Malomed, Boris A.; Zeng, Jianhua
Abstract: Solitons in the fractional space, supported by lattice potentials, have recently attracted much interest. The limit of deep 1D and 2D lattices in this system is considered, featuring finite bandgaps separated by nearly flat Bloch bands. Such spectra are also a subject of great interest in current studies. The existence, shapes, and stability of various localized modes, including fundamental gap and vortex solitons, are investigated by means of numerical methods; some results are also obtained with the help of analytical approximations. In particular, the 1D and 2D gap solitons, belonging to the first and second finite bandgaps, are tightly confined around a single cell of the deep lattice. Vortex gap solitons are constructed as four‐peak "squares" and "rhombuses" with imprinted winding number S = 1 S=1 . Stability of the solitons is explored by means of the linearization and verified by direct simulations. Abstract : Periodic potentials provide an intriguing platform for studying solitons in the framework of the associated linear‐Bloch spectrum. Here, various 1D and 2D localized modes are theoretically and numerically addressed in nonlinear fractional systems with deep lattices, including fundamental gap solitons and vortices, revealing rich soliton physics in first and second bandgaps of deep lattices using full continuous mean‐ field model beyond tight‐binding approximation.