Communications in Mathematical Sciences
Volume 5 (2007)
A Hermite pseudo-spectral method for solving systems of Gross-Pitaevskii equations
Pages: 299 – 312
We propose and analyze discretization methods for solving finite systems of nonlinearly coupled Schrödinger equations, which arise as an asymptotic limit of the three-dimensional Gross-Pitaevskii equation with strongly anisotropic potential. A pseudo-spectral method with Hermite basis functions combined with a Crank-Nicolson type method is introduced. Numerical experiments are presented, including a comparison with an alternative discretization approach.
Gross-Pitaevskii equation; spectral decomposition; Fourier expansion; Hermite polynomials
2010 Mathematics Subject Classification
33C45, 35Q55, 65M70