Scattering operator for the fourth order nonlinear Schrüdinger equation

Abstract

We study the fourth order nonlinear Schrodinger equation \begin{equation*} i{\partial }_{t}u-\frac{1}{4}\partial _{x}^{4}u=f(u) ,\quad (t,x)\in \mathbb{R}\times \mathbb{R}, \end{equation*} where $f(u) $ is the power nonlinearity of order $p>5.$ The scattering operator is constructed in a neighborhood of the origin in a sutable weighted Sobolev space.