Nonlinearity Management in Higher Dimensions

Details Nonlinearity Management in Higher Dimensions Nonlinearity Management in Higher Dimensions

2005-05-20

arxiv.org/abs/cond-mat/0505498v1

Physics

Condensed Matter

Superconductivity

9 pages, 1 figures

Scientific paper

10.1088/0305-4470/39/3/002

In the present short communication, we revisit nonlinearity management of the time-periodic nonlinear Schrodinger equation and the related averaging procedure. We prove that the averaged nonlinear Schrodinger equation does not support the blow-up of solutions in higher dimensions, independently of the strength in the nonlinearity coefficient variance. 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.

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