Numerical Calculation of Monotonicity Properties of the Blow-Up Time of NLS (Communications in Computational Physics, 2018)
We investigate blow-up of the focusing nonlinear Schr ¨odinger equation, inthe critical and supercritical cases. Numerical simulations are performed to examinethe dependence of the time at which blow-up occurs on properties of the data or theequation. Three cases are considered: dependence on the scale of the nonlinearitywhen the initial data are fixed; dependence upon the strength of a quadratic oscillationin the initial data when the equation and the initial profile are fixed; and dependenceupon 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.