Electron. J. Diff. Equ., Vol. 2010(2010), No. 89, pp. 1-12.

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

Marco Caliari, Marco Squassina

Abstrac: 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.

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Marco Caliari
Dipartimento di Informatica
Università degli Studi di Verona
Cá Vignal 2, Strada Le Grazie 15, I-37134 Verona, Italy
email: marco.caliari@univr.it
Marco Squassina
Dipartimento di Informatica
Università degli Studi di Verona
Cá Vignal 2, Strada Le Grazie 15, I-37134 Verona, Italy
email: marco.squassina@univr.it

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