Threshold even solutions to the nonlinear Schr\"{o}dinger equation with delta potential at high frequencies

TL;DR

This paper studies the behavior of symmetric solutions to a nonlinear Schrödinger equation with a delta potential, focusing on their dynamics at high frequencies and classifying their long-term behavior.

Contribution

It provides a classification of the global dynamics of even solutions with high-frequency ground state action in the presence of a delta potential.

Findings

Classification of global dynamics for even solutions

Analysis of high-frequency behavior

Insights into the impact of delta potential on solution stability

Abstract

We consider the nonlinear Schr\"{o}dinger 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.