On the blow-up threshold for weakly coupled nonlinear Schroedinger equations

Details On the blow-up threshold for weakly coupled nonlinear Schroedinger equations On the blow-up threshold for weakly coupled nonlinear Schroedinger equations

2007-05-03

arxiv.org/abs/0705.0491v1

Mathematics

Analysis of PDEs

14 pages

Scientific paper

10.1088/1751-8113/40/47/007

We study the Cauchy problem for a system of two coupled nonlinear focusing
Schroedinger equations arising in nonlinear optics. We discuss when the
solutions are global in time or blow-up in finite time. Some results, in
dependence of the data of the problem, are proved; in particular we give a
bound, depending on the coupling parameter, for the blow-up threshold.

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