Monotonicity properties of blow-up time for nonlinear Schr\"{o}dinger equation: numerical tests
Analysis of PDEs
2016-08-16 v2 Numerical Analysis
Abstract
We consider the focusing nonlinear Schr\"{o}dinger equation, in the -critical and supercritical cases. We investigate numerically the dependence of the blow-up time on a parameter in three cases: dependence upon the coupling constant, 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; finally, dependence upon a damping factor when the initial data are fixed. It turns out that in most situations monotonicity in the evolution of the blow-up time does not occur. In the case of quadratic oscillations in the initial data, with critical nonlinearity, monotonicity holds; this is proven analytically.
Cite
@article{arxiv.math/0603107,
title = {Monotonicity properties of blow-up time for nonlinear Schr\"{o}dinger equation: numerical tests},
author = {Christophe Besse and Rémi Carles and Norbert Mauser and Hans-Peter Stimming},
journal= {arXiv preprint arXiv:math/0603107},
year = {2016}
}