Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 90, pp. 115.
Selfsimilar solutions with compactly supported profile of some
nonlinear Schrodinger equations
Pascal Begout, Jesus Ildefonso Diaz
Abstract:
``Sharp localized'' solutions (i.e. with compact support for each given time t)
of a singular nonlinear type Schr\"odinger equation in the whole space
are constructed here under the assumption that they have
a selfsimilar structure. It requires the assumption that the external
forcing term satisfies that
for some complex exponent
and for some profile function
which is assumed to be with compact support in
.
We show the existence of solutions of the form
,
with a profile
,
which also has compact support in
.
The proof of the localization of the support of the profile
uses some suitable energy method applied to the stationary problem satisfied
by
after some unknown transformation.
Submitted December 9, 2013. Published April 2, 2014.
Math Subject Classifications: 35B99, 35A01, 35A02, 35B65, 35J60.
Key Words: Nonlinear selfsimilar Schrodinger equation; compact support;
energy method.
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Pascal Bégout
Institut de Mathématiques de Toulouse & TSE
Université Toulouse I Capitole,
Manufacture des Tabacs
21, Allée de Brienne,
31015 Toulouse Cedex 6, France
email: Pascal.Begout@math.cnrs.fr


Jesús Ildefonso Díaz
Departamento de Matemática Aplicada
Instituto de Matemática Interdisciplinar
Universidad Complutense de Madrid
Plaza de las Ciencias, 3, 28040 Madrid, Spain
email: diaz.racefyn@insde.es

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