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EnglishWe 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
http://hdl.handle.net/11384/56060| Titolo: | Solutions to the nonlinear Schrodinger equation carrying momentum along acurve. |
| Autori interni: | MALCHIODI, ANDREA |
| Data di pubblicazione: | 2009 |
| Rivista: | COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS |
| Abstract: | 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 |
| Handle: | http://hdl.handle.net/1234/56060 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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