Persistence of solutions to higher order nonlinear Schrödinger equation

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