Persistence of solutions to the Derivative Nonlinear Schr\"odinger equation in weighted Sobolev spaces

TL;DR

This paper proves that solutions to the derivative nonlinear Schrödinger equation persist over time when starting from initial data in specific weighted Sobolev spaces, extending understanding of solution stability.

Contribution

It establishes the persistence property for solutions in weighted Sobolev spaces for the first time for this equation.

Findings

Solutions persist in weighted Sobolev spaces for initial data in specified spaces.

Extends previous results on solution stability to a broader class of initial conditions.

Provides mathematical foundation for further analysis of the derivative nonlinear Schrödinger equation.

Abstract

In this paper we show the persistence property for solutions of the derivative nonlinear Schr\"odinger equation with initial data in weighted Sobolev spaces $H^{2}(\mathbb{R})\cap L^2(|x|^{2r}dx)$, $r\in (0,1]$.