×

On the formation of singularities in solutions of the critical nonlinear Schrödinger equation. (English) Zbl 1007.35087

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.

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
PDF BibTeX XML Cite
Full Text: DOI