On asymptotic stability of ground states of NLS with a finite bands periodic potential in 1D
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- by Scipio Cuccagna and Nicola Visciglia PDF
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Abstract:
We consider a nonlinear Schrödinger equation \begin{equation*} iu_{t} -h_{0}u + \beta ( |u|^{2} )u=0 , (t,x)\in \mathbb {R}\times \mathbb {R}, \end{equation*} with $h_{0}= -\frac {d^{2}}{dx^{2}} +P(x)$ a Schrödinger operator with finitely many spectral bands. We assume the existence of an orbitally stable family of ground states. Exploiting dispersive estimates in Cuccagna (2008), Cuccagna and Visciglia (2009), and following the argument in Cuccagna (to appear) we prove that under appropriate hypotheses the ground states are asymptotically stable.References
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Additional Information
- Scipio Cuccagna
- Affiliation: DISMI, University of Modena and Reggio Emilia, via Amendola 2, Padiglione Morselli, Reggio Emilia 42100 Italy
- Email: cuccagna.scipio@unimore.it
- Nicola Visciglia
- Affiliation: Dipartimento di Matematica “L. Tonelli”, University of Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy
- Email: viscigli@dm.unipi.it
- Received by editor(s): September 27, 2008
- Published electronically: November 19, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 2357-2391
- MSC (2010): Primary 35Q55
- DOI: https://doi.org/10.1090/S0002-9947-2010-05046-9
- MathSciNet review: 2763720