Threshold odd solutions to the nonlinear Schrödinger equation in one dimension

We consider odd solutions to the Schr & ouml;dinger equation with the L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>{2}$$\end{document}-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 that of the ground state. In the present paper, we show that odd solutions with action twice that of the ground state scatter or blow up.