A G-FDTD scheme for solving multi-dimensional open dissipative Gross-Pitaevskii equations
Abstract
Behaviors of dark soliton propagation, collision, and vortex formation in the context of a non-equilibrium condensate are interesting to study. This can be achieved by solving open dissipative Gross-Pitaevskii equations (dGPEs) in multiple dimensions, which are a generalization of the standard Gross-Pitaevskii equation that includes effects of the condensate gain and loss. In this article, we present a generalized finite-difference time-domain (G-FDTD) scheme, which is explicit, stable, and permits an accurate solution with simple computation, for solving the multi-dimensional dGPE. The scheme is tested by solving a steady state problem in the non-equilibrium condensate. Moreover, it is shown that the stability condition for the scheme offers a more relaxed time step restriction than the popular pseudo-spectral method. The G-FDTD scheme is then employed to simulate the dark soliton propagation, collision, and the formation of vortex-antivortex pairs.
- Publication:
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Journal of Computational Physics
- Pub Date:
- February 2015
- DOI:
- 10.1016/j.jcp.2014.11.021
- Bibcode:
- 2015JCoPh.282..303M
- Keywords:
-
- Finite-difference time-domain (FDTD) scheme;
- Gross-Pitaevskii equation (GPE);
- Dark soliton;
- Stability;
- Non-equilibrium condensate