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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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Official URL: http://www.sciencedirect.com/science/article/pii/S1631073X06000550

## 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 |
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Uncontrolled Keywords: | singular complex potentials |

Subjects: | Sciences > Mathematics > Mathematical analysis Sciences > Mathematics > Differential geometry |

ID Code: | 15411 |

Deposited On: | 29 May 2012 09:27 |

Last Modified: | 12 Dec 2018 15:07 |

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