Abstract
This paper obtains the numerical solutions of the elliptic solitons in a (1+2)-dimensional anisotropic nonlocal nonlinear fractional Schrodinger equation, and verifies their stabilities by the direct propagation method. The results show that the properties of such solitons relatively depend on the Levy index. Such as the soliton shape varies with the change of Levy index. When the Levy 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 Levy index.
Highlights
Fractional calculus is a useful tool in mathematics, physics and engineering [1]–[5] for that it can describes many complex phenomena
The profiles of elliptic solitons for different Levy indexes are obtained by using the iteration algorithm which was presented by Qi Guo [36]
When α = 1.2, the propagation dynamics of elliptic solitons was shown in Fig. 1(b) and (d)
Summary
Fractional calculus is a useful tool in mathematics, physics and engineering [1]–[5] for that it can describes many complex phenomena. W. Islam has obtained the solitons in time fractional nonlinear Schrodinger equation with competing weakly nonlocal nonlinearity [7]. The elliptical optical beams is generalized and readily achieved in experiment, and the nonlocal media with anisotropic has been found in the available materials, such as lead glass [31] and nematic liquid crystal [32], [33]. This manuscript combines the fractional diffraction effect and anisotropic (1+2)dimensional nonlocal effect for the first time in optics area, obtains the elliptic and higher-order elliptic solitons. The physical features, which exhibited by the elliptic solitons for different Levy indexes, been studied
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