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arXiv · 1512.01441

Numerical solution of the stationary multicomponent nonlinear Schr\"{o}dinger equation with a constraint on the angular momentum

P. Sandin·M. Ogren·M. Gulliksson
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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.

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P. Sandin, M. Ogren, M. Gulliksson. 2015-12-04. Numerical solution of the stationary multicomponent nonlinear Schr\"{o}dinger equation with a constraint on the angular momentum. https://doi.org/10.1103/physreve.93.033301

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