Abstract

The focusing nonlinear Schrödinger equation arises in various physical phenomena and it is therefore of interest to determine mathematical conditions on the initial data that guarantee whether the corresponding solution will blow up in finite time or exist globally in time. We focus on solutions to the mass‐supercritical nonlinear Schrödinger equation (1) in 1D case. In particular, we investigate numerical thresholds between blow up and scattering of solutions in the focusing NLS equation as well as rates and profiles of blow up solutions. We consider several initial data families and the degree of nonlinearity p>5.

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