Publication Date
2006
Journal or Book Title
Journal of Physics A: Mathematical and General
Abstract
In the present paper, we revisit nonlinearity management of the time-periodic nonlinear Schrödinger equation and the related averaging procedure. By means of rigorous estimates, we show that the averaged nonlinear Schrödinger equation does not blow up in the higher dimensional case so long as the corresponding solution remains smooth. In particular, we show that the H1 norm remains bounded, in contrast with the usual blow-up mechanism for the focusing Schrödinger equation. This conclusion agrees with earlier works in the case of strong nonlinearity management but contradicts those in the case of weak nonlinearity management. The apparent discrepancy is explained by the divergence of the averaging procedure in the limit of weak nonlinearity management.
Pages
479-
Volume
39
Issue
3
Recommended Citation
Kevrekidis, PG, "Nonlinearity management in higher dimensions" (2006). Journal of Physics A: Mathematical and General. 1086.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1086
Comments
This is the pre-published version harvested from arXiv. The published version is located at http://iopscience.iop.org/0305-4470/39/3/002/