On the Dynamics of solitons in the nonlinear Schroedinger equation

We study the behavior of the soliton solutions of the equation i((\partialψ)/(\partialt))=-(1/(2m))Δψ+(1/2)W_{ε}'(ψ)+V(x)ψ where W_{ε}' is a suitable nonlinear term which is singular for ε=0. We use the "strong" nonlinearity to obtain results on existence, shape, stability and dynamics of the soliton. The main result of this paper (Theorem 1) shows that for ε\to0 the orbit of our soliton approaches the orbit of a classical particle in a potential V(x).

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