Kavian, Otared; Weissler, Fred B. Self-similar solutions of the pseudo-conformally invariant nonlinear Schrödinger equation. (English) Zbl 0809.35125 Mich. Math. J. 41, No. 1, 151-173 (1994). The nonlinear Schrödinger equation \[ iu_ t+ \Delta u+ \varepsilon| u|^ \alpha u=0, \qquad x\in\mathbb{R}^ n \tag{1} \] is investigated. A solution \(u\) of (1) is self-similar if \(u(x,t)= \lambda^{-i\omega+ 2/\alpha} u(\lambda^ 2 t,\lambda t)\) for all \(\lambda>0\) and some fixed \(\omega\in \mathbb{R}\). In this paper the critical power \(\alpha= 4/n\) is considered. Reviewer: L.A.Sakhnovich (Odessa) Cited in 1 ReviewCited in 37 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) Keywords:critical power; nonlinear Schrödinger equation PDFBibTeX XMLCite \textit{O. Kavian} and \textit{F. B. Weissler}, Mich. Math. J. 41, No. 1, 151--173 (1994; Zbl 0809.35125) Full Text: DOI