Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 89, pp. 1-12.

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

Authors: Marco Caliari   (Univ. degli Studi di Verona, Italy)
         Marco Squassina (Univ. degli Studi di Verona, Italy)

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 $\ddot x=-\nabla V(x)$.
 Finally, we provide examples and analyze the numerical errors
 in the two dimensional case when V is a harmonic potential.
 
Submitted March 5, 2010. Published June 25, 2010.
Math Subject Classifications: 35Q40, 58E30, 81Q05, 81Q20, 37N30.
Key Words: Nonlinear Schrodinger equations; ground states;
           soliton dynamics in an external potential;
           numerical computation of ground states; semi-classical limit.