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arXiv:0908.3648 [math.NA]AbstractReferencesReviewsResources

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

Marco Caliari, Marco Squassina

Published 2009-08-25, updated 2009-08-26Version 2

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.

Comments: 13 pages, 4 figures
Categories: math.NA
Subjects: 35Q40, 58E30, 81Q05, 81Q20, 37N30
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