We consider the initial value problem (IVP) associated to a higher order nonlinear Schr\"odinger (h-NLS) equation $ \partial_{ t}u+ia \partial^{ 2}_{ x}u+ b\partial^{ 3}_{ x}u+ic_1|u|^{ 2}u+c_2 |u|^{ 2}\partial_{ x}u=0, \quad x,t \in \mathbb{ R}, $ for given data in the modulation space $M_s^{ 2,p}(\mathbb{ R})$. Using ideias of Killip, Visan, Zhang, Oh, Wang, we prove that the IVP associated to the h-NLS equation is globally well-posed in the modulation spaces $M^{ s,p}$ for $s\geq\frac14$ and $p\geq2$.
Categories: math.AP