Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation

2021 ◽  
Vol 103 (3) ◽  
pp. 2493-2507
Author(s):  
Ahmed S. Hendy ◽  
Mahmoud A. Zaky
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Schrödinger Equation ◽  
Difference Method ◽  
Schrodinger Equation ◽  
Fractional Schrödinger Equation ◽  
Graded Meshes ◽  
Nonlinear Fractional Schrödinger Equation ◽  
Fractional Schrodinger Equation

Orbital stability of standing waves for nonlinear fractional Schrödinger equation with unbounded potential

2019 ◽  
Vol 12 (03) ◽  
pp. 1950043
Author(s):  
Xiaohua Liu
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Standing Waves ◽  
Orbital Stability ◽  
Fractional Schrödinger Equation ◽  
Unbounded Potential ◽  
Nonlinear Fractional Schrödinger Equation ◽  
The Stability ◽  
First Time ◽  
Fractional Schrodinger Equation

In this paper, the orbital stability of standing waves for nonlinear fractional Schrödinger equation is considered. By constructing the constrained functional extreme-value problem, the existence of standing waves is studied. With the help of the orbital stability theories presented by Grillakis, Shatah and Strauss, the orbital stability of standing waves is determined by the sign of a discriminant. To our knowledge, it is the first time that the abstract orbital stability theories presented by Grillakis, Shatah and Strauss are applied to study the stability of solutions for fractional evolution equation.

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