Numerical computation of soliton dynamics for NLS equations in a driving potential
This is an incremental numerical study for researchers in nonlinear waves and semiclassical analysis.
The paper numerically computes soliton dynamics for the nonlinear Schrödinger equation with an external potential, showing that the center of mass follows a Newtonian-type law in the semi-classical regime, with error analysis for harmonic potentials in 2D.
We provide some numerical computations for the soliton dynamics of the nonlinear Schrödinger 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.