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

Abstract: We consider the Gabitov-Turitsyn equation or the dispersion managed nonlinear Schr\"odinger equation of a power-type nonlinearity [ i\partial_t u+ d_\text{av} \partial_x^2u+\int_0^1 e^{-ir\partial_x^2}\big(|e^{ir\partial_x^2}u|^{p-1}e^{ir\partial_x^2}u\big)dr=0 ] and prove the global existence versus finite time blowup dichotomy for the mass-supercritical cases, that is, $p>9$.