RT Journal Article
T1 Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations
A1 Bègout, Pascal
A1 Díaz Díaz, Jesús Ildefonso
AB “Sharp localized” solutions (i.e. with compact support for each given time t) of a singular nonlinear type Schrödinger equation in the whole space R N are constructed here under the assumption that they have a self-similar structure. It requires the assumption that the external forcing term satisfies that f(t, x) = t−(p−2)/2F (t−1/2x) for some complex exponent p and for some profile function F which is assumed to be with compact support in R N . We show the existence of solutions of the form u(t, x) = t p/2U(t−1/2x), with a profile U, which also has compact support in R N . The proof of the localization of the support of the profile U uses some suitable energy method applied to the stationary problem satisfied by U after some unknown transformation.
PB Department of Mathematics  Texas State University
SN 1072-6691
YR 2014
FD 2014
LK https://hdl.handle.net/20.500.14352/33950
UL https://hdl.handle.net/20.500.14352/33950
LA eng
NO Unión Europea. FP7
NO DGISPI
NO UCM
DS Docta Complutense
RD 4 abr 2025