A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation

2014 ◽  
Vol 36 (6) ◽  
pp. A2865-A2886 ◽  
Author(s):  
Xuan Zhao ◽  
Zhi-zhong Sun ◽  
Zhao-peng Hao
Keyword(s):  
Schrödinger Equation ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Two Dimensional ◽  
Fractional Schrödinger Equation ◽  
Adi Scheme ◽  
Compact Adi Scheme ◽  
Fractional Schrodinger Equation

Dynamics of two-dimensional multi-peak solitons based on the fractional Schrödinger equation

2021 ◽  
Author(s):  
Xiaoping Ren ◽  
Fang Deng
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Optical Lattices ◽  
Two Dimensional ◽  
Fractional Schrödinger Equation ◽  
Existence Domain ◽  
Maximal Peak ◽  
Band Gap Structure ◽  
Fractional Schrodinger Equation ◽  
Peak Value

We address the propagation dynamics of two-dimensional multi-peak solitons in the optical lattices based on the fractional Schrödinger equation. The effect of Lévy index and lattice depth on the band-gap structure of optical lattices are presented. Two-, three-, four-, six- and eight-peak solitons all can exist in the first gap and be stable in a wide region of their existence domain. The effective width, maximal peak value and the power of soliton are also studied. It indicates that the Lévy index plays a significant role on the properties of solitons.

Solitons in the two-dimensional fractional Schrödinger equation with radially symmetric PT potential

Optik ◽  
2020 ◽  
Vol 202 ◽  
pp. 163652 ◽  
Author(s):  
Hexi Liang ◽  
Si-liu Xu ◽  
Wen-wu Deng ◽  
Yonghong Dai ◽  
Hong Li ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Two Dimensional ◽  
Fractional Schrödinger Equation ◽  
Fractional Schrodinger Equation
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