Numerical solution of the stationary multicomponent nonlinear Schr\"{o}dinger equation with a constraint on the angular momentum
Abstract
We formulate a damped oscillating particle method to solve the stationary nonlinear Schr\"{o}dinger equation (NLSE). The ground state solutions are found by a converging damped oscillating evolution equation that can be discretized with symplectic numerical techniques. The method is demonstrated for three different cases: for the single-component NLSE with an attractive self-interaction, for the single-component NLSE with a repulsive self interaction and a constraint on the angular momentum, and for the two-component NLSE with a constraint on the total angular momentum. We reproduce the so called yrast curve for the single-component case, described in [A. D. Jackson et al., Europhys. Lett. 95, 30002 (2011)], and produce for the first time an analogous curve for the two-component NLSE. The numerical results are compared with analytic solutions and competing numerical methods. Our method is well suited to handle a large class of equations and can easily be adapted to further constraints and components.
Keywords
Cite
@article{arxiv.1512.01441,
title = {Numerical solution of the stationary multicomponent nonlinear Schr\"{o}dinger equation with a constraint on the angular momentum},
author = {P. Sandin and M. Ogren and M. Gulliksson},
journal= {arXiv preprint arXiv:1512.01441},
year = {2016}
}