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

Abstract

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.

14 pages

References in corpus (1)

• Finite time collapse of N classical fields described by coupled nonlinear Schrodinger equations

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