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 . 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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