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

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 $0\le \theta \le 1$.