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

TL;DR

This paper extends global existence and scattering results for higher order nonlinear Schrödinger equations with anisotropic dispersion to broader modulation spaces, generalizing previous work and establishing new analytical frameworks.

Contribution

It generalizes small data global existence and scattering results to more comprehensive modulation spaces for higher order anisotropic NLS equations.

Findings

Established global existence for broader modulation spaces.

Proved scattering results in new functional settings.

Extended previous results to higher order anisotropic dispersion.

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 $s > \frac{d}{q'}$ and to the nonlinear Schr\"odinger equation with higher order anisotropic dispersion.