Uniqueness of a Minimizer for a Variational Problem Related to the Dispersion Managed Nonlinear Schrödinger Equation.

We consider a nonlocal and nonlinear minimization problem, with a parameter > 0, related to the dispersion managed nonlinear Schro"\dinger equation having a positive average dispersion. The minimizers converge, up to shifts and boosts, to a minimizer for the limit problem associated with the nonlinear Schro"\dinger equation in H1(R) as \varepsilon \rightarrow 0. Furthermore, the uniqueness of a minimizer for the minimization problem, up to shifts and boosts, is shown when \varepsilon is small enough.