We prove existence of a special class of solutions to an (elliptic) nonlinear Schrödinger equation on a manifold or in Euclidean space. Here V represents the potential, p an exponent greater than 1, and " a small parameter corresponding to the Planck constant. As " tends to 0 (in the semiclassical limit) we exhibit complex-valued solutions that concentrate along closed curves and whose phases are highly oscillatory. Physically these solutions carry quantum-mechanical momentum along the limit curves
Titolo: | Solutions to the nonlinear Schrodinger equation carrying momentum along acurve. | |
Autori: | ||
Data di pubblicazione: | 2009 | |
Rivista: | ||
Handle: | http://hdl.handle.net/1234/56060 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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