Domain walls in fractional media

Abstract

Currently, much interest is drawn to the analysis of optical and matter-wave modes supported by the fractional diffraction in nonlinear media. We predict a new type of such states, in the form of domain walls (DWs) in the two-component system of immiscible fields. Numerical study of the underlying system of fractional nonlinear Schroedinger equations demonstrates the existence and stability of DWs at all values of the respective Levy index (a < 2) which determines the fractional diffraction, and at all values of the XPM/SPM ratio b in the two-component system above the immiscibility threshold. The same conclusion is obtained for DWs in the system which includes the linear coupling, alongside the XPM interaction between the immiscible components. Analytical results are obtained for the scaling of the DW's width. The DW solutions are essentially simplified in the special case of b = 3, as well as close to the immiscibility threshold. In addition to symmetric DWs, asymmetric ones are constructed too, in the system with unequal diffraction coefficients and/or different Levy indices of the two components.

to be published in Physical Review E

References in corpus (6)

• 39-K Bose-Einstein condensate with tunable interactions
• Spatiotemporal accessible solitons in fractional dimensions
• Soliton dynamics in a fractional complex Ginzburg-Landau model
• Propagation dynamics of the circular Airy Gaussian vortex beams in the fractional nonlinear Schrödinger equation
• The Two-Dimensional Fractional Discrete Nonlinear Schrodinger Equation
• Perturbation Theory for Propagating Magnetic Droplet Solitons