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.


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
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