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We provide some numerical computations for the soliton dynamics of thenonlinear Schr\"odinger equation with an external potential. After computingthe ground state solution $r$ of a related elliptic equation we show that, inthe semi-classical regime, the center of mass of the solution with initialdatum modelled on $r$ is driven by the solution of a Newtonian type law.Finally, we provide some examples and analyze the numerical errors in the twodimensional case when $V$ is an harmonic potential.

Numerical computation of soliton dynamics for NLS equations in a driving potential