Geodesic
Numerical computation of soliton dynamics for NLS equations in a driving potential
Electronic journal of differential equations, Tome 2010 (2010)
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__a243,
     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},
     year = {2010},
     volume = {2010},
     zbl = {1196.35200},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a243/}
}
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%A Squassina,  Marco
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%J Electronic journal of differential equations
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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__a243/