The global Cauchy problem for the NLS with higher order anisotropic dispersion

We use a method developed by Strauss to obtain global wellposedness results in the mild sense for the small data Cauchy problem in modulation spaces $M_{p,q}^s(\mathbb{R}^d)$, where $q=1$ and $s\geq0$ or $q\in(1,\infty]$ and $s>\frac{d}{q'}$ for a nonlinear Schr\"odinger equation with higher order anisotropic dispersion and algebraic nonlinearities.