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arXiv · 2412.06962

Scattering and Blow-Up in Both Time Directions Above the Ground State for the Focusing Nonlinear Schr\"{o}dinger Equation

Ian Miller
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Abstract

In this article we obtain new scattering and blow-up solutions for intercritical focusing nonlinear Schr\"{o}dinger equations (NLS) above the ground state mass-energy threshold. The main focus of this article is the establishment of some solutions with arbitrarily large mass-energy which scatter in both time directions. In particular, large mass-energy which does not arise from the Galilean transformation. We additionally obtain new criteria for blow-up in both time directions, as well as improved sufficient conditions for scattering and blow-up in one time direction.

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Ian Miller. 2024-12-09. Scattering and Blow-Up in Both Time Directions Above the Ground State for the Focusing Nonlinear Schr\"{o}dinger Equation. https://arxiv.org/abs/2412.06962

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