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

## TL;DR

This paper proves global well-posedness for a nonlinear Schrödinger equation with higher order anisotropic dispersion using modulation spaces, extending previous methods to handle small initial data.

## Contribution

It introduces a novel application of Strauss's method to establish global solutions in modulation spaces for anisotropic NLS with algebraic nonlinearities.

## Key findings

- Global well-posedness in modulation spaces for small data
- Extension of Strauss's method to anisotropic dispersion
- Applicable to nonlinearities with algebraic growth

## 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 $s\geq0$ or $q\in(1,\infty]$ and $s>\frac{d}{q'}$ for a nonlinear Schr\"odinger equation with higher order anisotropic dispersion and algebraic nonlinearities.