scholarly journals On Fourier Time-Splitting Methods for Nonlinear Schrödinger Equations in the Semiclassical Limit

2013 ◽  
Vol 51 (6) ◽  
pp. 3232-3258 ◽  
Author(s):  
Rémi Carles
Keyword(s):  
Semiclassical Limit ◽  
Splitting Methods ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Time Splitting

scholarly journals Efficient time-splitting Hermite-Galerkin spectral method for the coupled nonlinear Schrödinger equations

2020 ◽  
Vol 14 ◽  
pp. 174830262097353
Author(s):  
Qingqu Zhuang ◽  
Yi Yang
Keyword(s):  
Splitting Method ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Time Step ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Time Splitting ◽  
Coupled Nonlinear Schrodinger Equations

The paper focuses on efficient time-splitting Hermite-Galerkin spectral approximation of the coupled nonlinear Schrödinger equations on the whole line. The original problem is decomposed into one nonlinear subproblem and one linear subproblem by time-splitting method. At each time step, the nonlinear subproblem is solved exactly. While the linear subproblem is efficiently solved by choosing suitable Hermite basis functions with matrix decomposition technique. Numerical experiments are carried out to demonstrate the effectiveness and efficiency of the proposed method.

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