The Nonlinear Schr\"odinger-Airy equation in weighted Sobolev spaces

TL;DR

This paper investigates the persistence of solutions to the nonlinear Schr"odinger-Airy equation within weighted Sobolev spaces, focusing on initial data with specific regularity and decay properties.

Contribution

It establishes the persistence property of solutions in weighted Sobolev spaces for the nonlinear Schr"odinger-Airy equation using the contraction principle.

Findings

Solutions persist in weighted Sobolev spaces under given initial conditions

The analysis applies to initial data in $H^{1/4}( ) igcap L^2(|x|^{2m}dx)$ with $0<m extless 1/8$

The contraction principle is used to prove the persistence property

Abstract

We study the persistence property of the solution for the nonlinear Schr\"odinger-Airy equation with initial data in the weighted Sobolev space $H^{1/4}(\mathbb{R})\cap L^2(|x|^{2m}dx)$, $0<m \leq 1/8$, via the contraction principle.