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

TL;DR

This paper investigates the conditions under which solutions to a system of coupled nonlinear Schrödinger equations either exist globally or blow up in finite time, providing bounds related to the coupling parameter.

Contribution

It introduces a new bound on the blow-up threshold for coupled nonlinear Schrödinger equations depending on the coupling parameter.

Findings

Derived a bound for blow-up threshold based on coupling strength

Identified conditions for global existence versus finite-time blow-up

Analyzed the influence of initial data on solution behavior

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.