The Nonlinear Schroedinger equation: solitons dynamics

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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 the soliton approximately follows the dynamics of a point particle, namely, the motion of its barycenter qₕ(t) satisfies the equation ddotqₕ(t)+∇ V(qₕ(t))=Hₕ(t) where ₜ∈ ᵣ |Hₕ(t)| -> 0 as h->0.