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

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.