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On a nonlinear Schrodinger equation with a localizing effect

Díaz Díaz, Jesús Ildefonso and Begout , Pascal (2006) On a nonlinear Schrodinger equation with a localizing effect. Comptes Rendus Mathematique, 342 (7). pp. 459-463. ISSN 1631-073X

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Abstract

We consider the nonlinear Schrodinger equation associated to a singular potential of the form a vertical bar u vertical bar(-(1-m))u + bu, for some In is an element of (0, 1), on a possible unbounded domain. We use some suitable energy methods to prove that if Re(a) + Im(a) > 0 and if the initial and right hand side data have compact support then any possible solution must also have a compact support for any t > 0. This property contrasts with the behavior of solutions associated to regular potentials (m >= 1). Related results are proved also for the associated stationary problem and for self-similar Solution on the whole space and potential a vertical bar u vertical bar(-(1-m)u). The existence of solutions is obtained by some compactness methods under additional conditions.


Item Type:Article
Uncontrolled Keywords:singular complex potentials
Subjects:Sciences > Mathematics > Mathematical analysis
Sciences > Mathematics > Differential geometry
ID Code:15411
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Deposited On:29 May 2012 09:27
Last Modified:06 Feb 2014 10:24

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