In this paper we investigate the dynamics of solitons occurring in the nonlinear Schroedinger equation when a parameter h → 0. We prove that under suitable assumptions, the soliton approximately follows the dynamics of a point particle, namely, the motion of its barycenter q(t) satisfies the equation q'' ( t ) + ∇ V (q(t))=H(t) where sup_t |H(t)| goes to 0 while h tends to 0.
The nonlinear Schroedinger equation: Soliton dynamics
BENCI, VIERI;GHIMENTI, MARCO GIPO;MICHELETTI, ANNA MARIA
2010-01-01
Abstract
In this paper we investigate the dynamics of solitons occurring in the nonlinear Schroedinger equation when a parameter h → 0. We prove that under suitable assumptions, the soliton approximately follows the dynamics of a point particle, namely, the motion of its barycenter q(t) satisfies the equation q'' ( t ) + ∇ V (q(t))=H(t) where sup_t |H(t)| goes to 0 while h tends to 0.File in questo prodotto:
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