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# Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result

 dc.contributor.author Mahmoudi, Fethi en_US dc.contributor.author Malchiodi, Andrea en_US dc.date.accessioned 2007-09-17T08:58:18Z en_US dc.date.accessioned 2011-09-07T20:28:05Z dc.date.available 2007-09-17T08:58:18Z en_US dc.date.available 2011-09-07T20:28:05Z dc.date.issued 2007-09-17T08:58:18Z en_US dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/2111 en_US dc.description.abstract We 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. en_US dc.format.extent 663755 bytes en_US dc.format.mimetype application/pdf en_US dc.language.iso en_US en_US dc.relation.ispartofseries SISSA;52/2007/M en_US dc.relation.ispartofseries arXiv.org;0708.0104 en_US dc.title Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result en_US dc.type Preprint en_US dc.contributor.department Functional Analysis and Applications en_US dc.contributor.area Mathematics en_US
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