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

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.

Keywords

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