Energy Scattering for the Generalized Davey-Stewartson Equations

Considering the generalized Davey-Stewartson equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i\mathop u\limits^. - \Delta u + \lambda \left| u \right|^p u + \mu E\left( {\left| u \right|^q } \right)\left| u \right|^{q - 2} u = 0$$\end{document} where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda > 0,\mu \ge 0,E ={\mathcal {F}}^{ - 1} \left( {\xi _1^2 /\left| \xi \right|^2 } \right){\mathcal{F}}$$\end{document} we obtain the existence of scattering operator in ∑(ℝn) := { u ∈ H1(ℝn) : |x|u ∈ L2(ℝn)}.