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We formulate a damped oscillating particle method to solve the stationarynonlinear Schr\"{o}dinger equation (NLSE). The ground state solutions are foundby a converging damped oscillating evolution equation that can be discretizedwith symplectic numerical techniques. The method is demonstrated for threedifferent cases: for the single-component NLSE with an attractiveself-interaction, for the single-component NLSE with a repulsive selfinteraction and a constraint on the angular momentum, and for the two-componentNLSE with a constraint on the total angular momentum. We reproduce the socalled yrast curve for the single-component case, described in [A. D. Jacksonet al., Europhys. Lett. 95, 30002 (2011)], and produce for the first time ananalogous curve for the two-component NLSE. The numerical results are comparedwith analytic solutions and competing numerical methods. Our method is wellsuited to handle a large class of equations and can easily be adapted tofurther constraints and components.

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