Threshold odd solutions to the nonlinear Schr\"{o}dinger equation in one dimension
Analysis of PDEs
2022-03-10 v1
Abstract
We consider odd solutions to the Schr\"{o}dinger equation with the -supercritical power type nonlinearity in one dimensional Euclidean space. It is known that the odd solution scatters or blows up if its action is less than twice as that of the ground state. In the present paper, we show that the odd solutions with the action as twice as that of the ground state scatter or blow up.
Keywords
Cite
@article{arxiv.2203.04495,
title = {Threshold odd solutions to the nonlinear Schr\"{o}dinger equation in one dimension},
author = {Stephen Gustafson and Takahisa Inui},
journal= {arXiv preprint arXiv:2203.04495},
year = {2022}
}