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

Solutions to the nonlinear Schrodinger equation carrying momentum along acurve.

MALCHIODI, ANDREA;
2009

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
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/56060
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 20
  • ???jsp.display-item.citation.isi??? 20
social impact