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

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Author(s): Marco Caliari | Marco Squassina

Journal: Electronic Journal of Differential Equations
ISSN 1072-6691

Volume: 2010;
Issue: 89,;
Start page: 1;
Date: 2010;
Original page

Keywords: Nonlinear Schrodinger equations | ground states | soliton dynamics in an external potential | numerical computation of ground states | semi-classical limit

ABSTRACT
We provide numerical computations for the soliton dynamics of the nonlinear Schrodinger 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 built upon r is driven by the solution to $ddot x=- abla V(x)$. Finally, we provide examples and analyze the numerical errors in the two dimensional case when V is a harmonic potential.
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