Threshold even solutions to the nonlinear Schrödinger equation with delta potential at high frequencies

Stephen Gustafson; Takahisa Inui

doi:10.3934/dcds.2024054

Article Contents

2024, Volume 44, Issue 10: 3135-3176. Doi: 10.3934/dcds.2024054

This issue Previous Article Construction of unstable concentrated solutions of the Euler and gSQG equations Next Article On weighted Orlicz-Sobolev inequalities

Threshold even solutions to the nonlinear Schrödinger equation with delta potential at high frequencies

Stephen Gustafson^1, and
Takahisa Inui^{1, 2, ,}

1.
University of British Columbia, 1984 Mathematics Rd., Vancouver, Canada V6T1Z2
2.
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, Japan 560-0043

^*Corresponding author: Takahisa Inui
^*Corresponding author: Takahisa Inui

Received: March 2023

Revised: April 2024

Early access: May 12, 2024

Published online: May 12, 2024

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Abstract

We consider the nonlinear Schrödinger equation with a repulsive Dirac delta potential in one dimensional Euclidean space. We classify the global dynamics of even solutions with the same action as the high-frequency ground state standing wave solutions.

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Mathematics Subject Classification: Primary: 35Q55, 35B40, 35P25, 35B44.

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References

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