Global existence versus finite time blowup dichotomy for the dispersion managed NLS

Abstract

We consider the Gabitov–Turitsyn equation or the dispersion managed nonlinear Schrödinger equation of a power-type nonlinearity $i{\partial }_{t}u+d_{\mathrm{av}}{\partial }_x^{2}u+{\int }_0^1{e}^{-ir{\partial }_x^2}\left({\left|e^{ir{\partial }_x^2}u\right|}^{p-1}{e}^{ir{\partial }_x^2}u\right)dr=0$and prove the global existence versus finite time blowup dichotomy for the mass-supercritical cases, that is, $p>9$.