dc.contributor.author |
Mahmoudi, Fethi |
en_US |
dc.contributor.author |
Malchiodi, Andrea |
en_US |
dc.contributor.author |
Montenegro, Marcelo |
en_US |
dc.date.accessioned |
2007-09-17T09:14:27Z |
en_US |
dc.date.accessioned |
2011-09-07T20:28:05Z |
|
dc.date.available |
2007-09-17T09:14:27Z |
en_US |
dc.date.available |
2011-09-07T20:28:05Z |
|
dc.date.issued |
2007-09-17T09:14:27Z |
en_US |
dc.identifier.uri |
http://preprints.sissa.it/xmlui/handle/1963/2112 |
en_US |
dc.description.abstract |
We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroeodinger 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 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 is highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In this first part we provide the characterization of the limit set, with natural stationarity and non-degeneracy conditions. We then construct an approximate solution up to order $\epsilon^2$, showing that these conditions appear naturally in a Taylor expansion of the equation in powers of $\epsilon$. Based on these, an existence result will be proved in the second part. |
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dc.format.extent |
498331 bytes |
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dc.format.mimetype |
application/pdf |
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dc.language.iso |
en_US |
en_US |
dc.relation.ispartofseries |
SISSA;51/2007/M |
en_US |
dc.relation.ispartofseries |
arXiv.org;0708.0125 |
en_US |
dc.title |
Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part I: study of the limit set and approximate solutions |
en_US |
dc.type |
Preprint |
en_US |
dc.contributor.department |
Functional Analysis and Applications |
en_US |
dc.contributor.area |
Mathematics |
en_US |