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

Abstract

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 $s\ge 0$ or $q\in (1,\infty ]$ and $s>\frac{d}{q^{\prime }}$ for a nonlinear Schrödinger equation with higher order anisotropic dispersion and algebraic nonlinearities.

8 pages