Numerical study of time-splitting spectral discretizations of nonlinear Schrödinger equations in the semiclassical regimes. (English) Zbl 1038.65099

Bao, Weizhu; Jin, Shi; Markowich, Peter A.

SIAM J. Sci. Comput. 25, No. 1, 27-64 (2003).

MSC:

65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
81-08	Computational methods for problems pertaining to quantum theory
35Q40	PDEs in connection with quantum mechanics
81Q20	Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q55	NLS equations (nonlinear Schrödinger equations)
81Q05	Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics

Keywords:

nonlinear Schrödinger equation; time-splitting spectral approximation; semiclassical regime; meshing strategy; Gross-Pitaevskii equation; physical observable; numerical tests; stability; quantum hydrodynamics