The nonlinear Schroedinger equation: Solitons dynamics

In this paper we investigate the dynamics of solitons occurring in the nonlinear Schroedinger equation when a parameter h→0h→0.We prove that under suitable assumptions, the soliton approximately follows the dynamics of a point particle, namely, the motion of its barycenter  qh(t)qh(t) satisfies the equationq¨h(t)+∇V(qh(t))=Hh(t) wheresupt∈R|Hh(t)|→0ash→0.