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In this paper, we implement the Adaptive Moving Mesh method (AMM) to thesolution of initial value problems involving the Schr\"odinger equation, andmore specifically the Schr\"odinger-Poisson system of equations. This method isbased on the solution of the problem on a discrete domain, whose resolution iscoordinate and time-dependent, and allows to dynamically assign numericalresolution in terms of desired refinement criteria. We apply the method tosolve various test problems involving stationary solutions of the SP system,and toy scenarios related to the disruption of subhalo s made of ultralightbosonic dark matter traveling on top of host galaxies.

Solving the Schrodinger Poisson System using the coordinate Adaptive Moving Mesh method