Geodesic
Numerical computation of soliton dynamics for NLS equations in a driving potential
Electronic Journal of Differential Equations, Tome 2010 (2010).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We provide 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 built upon r is driven by the solution to ẍ = - V (x). Finally, we provide examples and analyze the numerical errors in the two dimensional case when V is a harmonic potential.
Classification : 35Q40, 58E30, 81Q05, 81Q20, 37N30
Keywords: nonlinear Schrödinger equations, ground states, soliton dynamics in an external potential, numerical computation of ground states, semi-classical limit 
@article{EJDE_2010__2010__a143,
     author = {Caliari, Marco and Squassina, Marco},
     title = {Numerical computation of soliton dynamics for {NLS} equations in a driving potential},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2010},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a143/}
}
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Caliari, Marco; Squassina, Marco. Numerical computation of soliton dynamics for NLS equations in a driving potential. Electronic Journal of Differential Equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a143/