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Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations

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Bègout, Pascal and Díaz Díaz, Jesús Ildefonso (2014) Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations. Electronic Journal of Differential Equations, 90 . pp. 1-15. ISSN 1072-6691

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Abstract

“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.


Item Type:Article
Subjects:Sciences > Mathematics > Differential equations
ID Code:29384
Deposited On:09 Apr 2015 08:00
Last Modified:12 Dec 2018 15:06

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