On the Dynamics of Solitons in the Nonlinear Schrodinger Equation

We study the behavior of the soliton solutions of the equation i partial derivative psi/partial derivative t = -1/2m Delta psi + 1/2 W '(epsilon) (psi) + v(x)psi where is a suitable nonlinear term which is singular for 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 epsilon -> 0 for the orbit of our soliton approaches the orbit of a classical particle in a potential V(x).