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

Pascal Bégout and Jesus Ildefonso Diaz

No 13-400, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: This paper deals with the study of "\textit{sharp localized}" solutions of a nonlinear type Schr\"odinger equation in the whole space $\R^N,$ $N\ge1,$ with a zero order term, in modulus, like a power $m$ less than one of the modulus of the solution, and with a non zero external forcing term $\f.$ Our fundamental assumption is that such an exponent $m$ verifies $m\in (0,1).$ The self-similar structure of the solution is justified from the assumption that the external forcing term satisfies that $\f(t,x)=t^{-(\vp-2)/2}\F(t^{-1/2}x)$ for some complex exponent $\vp$ and for some profile function $\F$ which is assumed to be with compact support in $\R^N.$ We show the existence of solutions $\vu(t,x)=t^{\vp/2}\U(t^{-1/2}x),$ with a profile $\U,$ which also have compact support in $\R^N,$ reason why we call as "\textit{sharp localized}" solutions to this type of solutions. 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.

Date: 2013-04
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/1301.0715v2.pdf Full text (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tse:wpaper:27182

Access Statistics for this paper

More papers in TSE Working Papers from Toulouse School of Economics (TSE) Contact information at EDIRC.
Bibliographic data for series maintained by ().