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Volume 5, Issue 2-4
Numerical Calculation of Monotonicity Properties of the Blow-Up Time of NLS

Hans Peter Stimming

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

Published online: 2009-02

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  • Abstract

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.

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@Article{CiCP-5-745, author = {Hans Peter Stimming}, title = {Numerical Calculation of Monotonicity Properties of the Blow-Up Time of NLS}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {2-4}, pages = {745--759}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7761.html} }
TY - JOUR T1 - Numerical Calculation of Monotonicity Properties of the Blow-Up Time of NLS AU - Hans Peter Stimming JO - Communications in Computational Physics VL - 2-4 SP - 745 EP - 759 PY - 2009 DA - 2009/02 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7761.html KW - AB -

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.

Hans Peter Stimming. (2009). Numerical Calculation of Monotonicity Properties of the Blow-Up Time of NLS. Communications in Computational Physics. 5 (2-4). 745-759. doi:
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