Higher-order NLS with anisotropic dispersion and modulation spaces: a global existence and scattering result

Abstract

Abstract In this paper we transfer a small data global existence and scattering result by Wang and Hudzik to the more general case of modulation spaces $M_{p, q}^s(\mathbb{R}^d)$ where q = 1 and $s \geq 0$ or $q \in (1, \infty]$ and $s \gt \frac{d}{q^{\prime}}$ and to the non-linear Schrödinger equation with higher-order anisotropic dispersion.