Commun. Comput. Phys., 5 (2009), pp. 745-759.


Numerical Calculation of Monotonicity Properties of the Blow-Up Time of NLS

Hans Peter Stimming 1*

1 Wolfgang Pauli Institute, c/o Institut fur Mathematik, Universitat Wien, Botzmanngasse 9, 1090 Wien, Austria.

Received 9 October 2007; Accepted (in revised version) 18 December 2007
Available online 1 August 2008

Abstract

We investigate blow-up of the focusing nonlinear Schrodinger equation, in the critical and supercritical cases. Numerical simulations are performed to examine the dependence of the time at which blow-up occurs on properties of the data or the equation. Three cases are considered: dependence on the scale of the nonlinearity when the initial data are fixed; dependence upon the strength of a quadratic oscillation in the initial data when the equation and the initial profile are fixed; and dependence upon a damping factor when the initial data are fixed. In most of these situations, monotonicity in the evolution of the blow-up time does not occur.

AMS subject classifications: 35Q55, 65M70, 81Q05

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Key words: Nonlinear Schrodinger equation, finite time blow-up, wave collapse.

*Corresponding author.
Email: hans.peter.stimming@univie.ac.at (H. P. Stimming)
 

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