Persistence of solutions to higher order nonlinear Schr\"odinger equation

TL;DR

This paper proves that solutions to the higher order nonlinear Schrödinger equation, also known as the Airy-Schrödinger equation, persist over time within certain weighted Sobolev spaces using an Abstract Interpolation Lemma.

Contribution

The paper introduces a method to demonstrate solution persistence in weighted Sobolev spaces for the higher order nonlinear Schrödinger equation.

Findings

Solutions persist in weighted Sobolev spaces for $0 \\le heta \\le 1$

Application of an Abstract Interpolation Lemma is effective

Extends understanding of solution behavior for higher order NLS equations

Abstract

Applying an Abstract Interpolation Lemma, we can show persistence of solutions of the initial value problem to higher order nonlinear Schr\"odinger equation, also called Airy-Schr\"odinger equation, in weighted Sobolev spaces $\mathcal{X}^{2,\theta}$, for $0 \le \theta \le 1$.