Scattering and Blow-up for threshold even solutions to the nonlinear Schrödinger equation with repulsive delta potential at low frequencies

2023/10/13 by Gustafson, Stephen, Inui, Takahisa
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.08859

Abstract

We consider the L²-supercritical nonlinear Schrödinger equation with a repulsive Dirac delta potential in one dimensional space. In a previous work, we clarified the global dynamics of even solutions with the same action as the high-frequency ground state standing wave solutions. In that case, there are obvious non-scattering global solutions, i.e., the standing waves. In this paper, we show a scattering and blow-up dichotomy for threshold even solutions in the low-frequency case. We emphasize that this dichotomy still holds at the critical frequency between high and low.

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