title: Numerical solution of the nonlinear Schrödinger equation using smoothed-particle hydrodynamics.
abstract: We formulate a smoothed-particle hydrodynamics numerical method, traditionally used for the Euler equations for fluid dynamics in the context of astrophysical simulations, to solve the nonlinear Schrödinger equation in the Madelung formulation. The probability density of the wave function is discretized into moving particles, whose properties are smoothed by a kernel function. The traditional fluid pressure is replaced by a quantum pressure tensor, for which a robust discretization is found. We demonstrate our numerical method on a variety of numerical test problems involving the simple harmonic oscillator, soliton-soliton collision, Bose-Einstein condensates, collapsing singularities, and dark matter halos governed by the Gross-Pitaevskii-Poisson equation. Our method is conservative, applicable to unbounded domains, and is automatically adaptive in its resolution, making it well suited to study problems with collapsing solutions.
authors.affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, USA.
authors.forename: Philip
authors.initials: P
authors.lastname: Mocz
authors.affiliation: Istituto per le Applicazioni del Calcolo, CNR, Viale del Policlinico 137, I-00161, Roma, Italy and Institute of Applied Computational Science, Harvard School of Engineering and Applied Sciences, Northwest B162, 52 Oxford Street, Cambridge, Massachusetts 02138, USA.
authors.forename: Sauro
authors.initials: S
authors.lastname: Succi