Monotonicity properties of blow-up time for nonlinear Schr\"{o}dinger   equation: numerical tests
  We consider the focusing nonlinear Schr\"{o}dinger equation, in the $L^2$-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. 
Christophe Besse (LPP, INRIA FUTURS), R\'emi Carles (MAB), Norbert   Mauser (ICP), Hans-Peter Stimming (ICP)