Perelman, Galina On the formation of singularities in solutions of the critical nonlinear Schrödinger equation. (English) Zbl 1007.35087 Ann. Henri Poincaré 2, No. 4, 605-673 (2001). The author considers the nonlinear Schrödinger equation \[ i\psi_{t}=-\psi -\left|\psi\right|^{4}\psi \] with initial data \(\psi|_{t=0}=\varphi+\kappa\), where \(\kappa\) is small in suitable sense. It is shown that for a certain set of initial perturbations \(\kappa\) the solution \(\psi\) blows up in finite time. An asymptotic representation of the solution is obtained. Reviewer: Vladislav Kravchenko (México) Cited in 1 ReviewCited in 53 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 35A20 Analyticity in context of PDEs 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics Keywords:nonlinear Schrödinger equation; initial perturbations; asymptotic representation PDF BibTeX XML Cite \textit{G. Perelman}, Ann. Henri Poincaré 2, No. 4, 605--673 (2001; Zbl 1007.35087) Full Text: DOI OpenURL