An L1 Legendre–Galerkin spectral method with fast algorithm for the two-dimensional nonlinear coupled time fractional Schrödinger equation and its parameter estimation

2021 ◽  
Vol 82 ◽  
pp. 13-35
Author(s):  
Junqing Jia ◽  
Xiaoyun Jiang ◽  
Hui Zhang
Keyword(s):  
Parameter Estimation ◽  
Schrödinger Equation ◽  
Spectral Method ◽  
Fast Algorithm ◽  
Schrodinger Equation ◽  
Two Dimensional ◽  
Fractional Schrödinger Equation ◽  
Galerkin Spectral Method ◽  
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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