Elliptic Solitons in (1+2)-Dimensional Anisotropic Nonlocal Nonlinear Fractional Schrödinger Equation

This paper obtains the numerical solutions of the elliptic solitons in a (1+2)-dimensional anisotropic nonlocal nonlinear fractional Schrödinger equation, and verifies their stabilities by the direct propagation method. The results show that the properties of such solitons relatively depend on the Lévy index. Such as the soliton shape varies with the change of Lévy index. When the Lévy index decreases, the ellipticity will increase, while the critical power will decrease. Furthermore, we demonstrate the physical features exhibited by the higher order elliptic solitons for a different Lévy index.