Multisymplectic structure-preserving scheme for the coupled Gross–Pitaevskii equations

Abstract

In this paper, we study numerically the dynamics of the rotating Bose–Einstein condensates (BECs) modelled by the coupled Gross–Pitaevskii (CGP) equations with angular momentum rotating terms. First, the multisymplectic structure of the CGP equations is investigated by introducing some canonical momenta which allows us to construct the corresponding multisymplectic schemes. Then applying the midpoint rule in both temporal and spatial directions, a multisymplectic scheme is proposed for the CGP equations. The conservative properties and the convergence analysis are discussed for the multisymplectic scheme. The cut-off function technique is utilized for the error estimation. Numerical examples are carried out to verify the conservative property and the convergence rate.

Keywords:

• Coupled Gross–Pitaevskii equations
• mu
  ltisymplectic Hamiltonian system
• conservation laws
• multisymplectic scheme

2010 Mathematics Subject Classifications:

• 65M06
• 65M12
• 70H15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Nos. 11771213,11961036), the Natural Science Foundation of Jiangxi Province (Nos. 20161ACB20006,20181BAB201008).