01231nas a2200109   4500008004300000245012500043210006900168520080600237100002001043700002201063856003601085       2007                        en_Ud  00aSolutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result0 aSolutions to the nonlinear Schroedinger equation carrying moment3 aWe prove existence of a special class of solutions to the (elliptic) Nonlinear Schroedinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$ on a manifold or in the Euclidean space. Here V represents the potential, p is an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase in highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In the first part of this work we identified the limit set and constructed approximate solutions, while here we give the complete proof of our main existence result.1 aMahmoudi, Fethi1 aMalchiodi, Andrea  uhttp://hdl.handle.net/1963/2111