Scattering for the focusing, $L^2$-supercritical fourth-order NLS in one dimension

Abstract

In this paper, we consider the fourth-order Schr\"odinger equations with focusing, $L^2$-supercritical nonlinearity in one dimension. We prove the global existence and scattering of solutions below the ground state threshold under the evenness assumption. This results extends to the result by Guo and Dinh in higher dimensions under the radial assumption.