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Asymptotic stability of ground states in 2D nonlinear Schrödinger equation including subcritical cases

Abstract:

We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$) nonlinearities. We study the asymptotic stability of the nonlinear bound states, i.e. periodic in time localized in space solutions. Our result shows that all solutions with small initial data, converge to a nonlinear bound state. Therefore, the nonlinear bound st...

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Publication status:
Published

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Publisher copy:
10.1016/j.jde.2009.04.015

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Journal:
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume:
247
Issue:
3
Pages:
710-735
Publication date:
2008-05-26
DOI:
EISSN:
1090-2732
ISSN:
0022-0396
URN:
uuid:f32cbda4-4234-4018-a39a-c3fd0a2543df
Source identifiers:
11187
Local pid:
pubs:11187
Language:
English
Keywords:

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