Multi-parameter continuation and collocation methods for rotating multi-component Bose–Einstein condensates

Abstract

We describe multi-parameter continuation methods combined with spectral collocation methods for computing numerical solutions of rotating two-component Bose–Einstein condensates (BECs), which are governed by the Gross–Pitaevskii equations (GPEs). Various types of orthogonal polynomials are used as the basis functions for the trial function space. A novel multi-parameter/multiscale continuation algorithm is proposed for computing the solutions of the governing GPEs, where the chemical potential of each component and angular velocity are treated as the continuation parameters simultaneously. The proposed algorithm can effectively compute numerical solutions with abundant physical phenomena. Numerical results on rotating two-component BECs are reported.

Keywords:

• spectral collocation method
• Gross–Pitaevskii equation
• Legendre polynomials
• Lagrange interpolation
• two-component BECs

2010 AMS Subject Classifications::

• 65N35
• 35P30
• 35Q55

Acknowledgements

Supported by the National Science Council of R.O.C. (Taiwan) through Project NSC 101-2115-M-231-001-MY2.