Global existence versus finite time blowup dichotomy for the dispersion managed NLS
arXiv:2311.02905
Abstract
We consider the Gabitov-Turitsyn equation or the dispersion managed nonlinear Schrödinger 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, .
23pages. 1 figure