We investigate blow-up of the focusing nonlinear Schr¨odinger equation,in the critical and supercritical cases.Numerical simulations are performed to examine the dependence of the time at which blow-up occurs on ...We investigate blow-up of the focusing nonlinear Schr¨odinger 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.展开更多
基金This work was supported by the Austrian Science Foundation(FWF)via the START project(Y-137-TEC)by theWWTF(Viennese Science Fund,project MA-45).
文摘We investigate blow-up of the focusing nonlinear Schr¨odinger 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.
