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

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

2009-08-25

arxiv.org/abs/0908.3648v2

Mathematics

Numerical Analysis

13 pages, 4 figures

Scientific paper

We provide some numerical computations for the soliton dynamics of the nonlinear Schr\"odinger equation with an external potential. After computing the ground state solution $r$ of a related elliptic equation we show that, in the semi-classical regime, the center of mass of the solution with initial datum 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 two dimensional case when $V$ is an harmonic potential.

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