Energy Scattering for the Generalized Davey-Stewartson Equations

Abstract

Considering the generalized Davey-Stewartson equation $$i\mathop u\limits^. - \Delta u + \lambda \left| u \right|^p u + \mu E\left( {\left| u \right|^q } \right)\left| u \right|^{q - 2} u = 0$$ where $$\lambda > 0,\mu \ge 0,E ={\mathcal {F}}^{ - 1} \left( {\xi _1^2 /\left| \xi \right|^2 } \right){\mathcal{F}}$$ we obtain the existence of scattering operator in ∑(ℝ n ) := { u ∈ H 1(ℝ n ) : |x|u ∈ L 2(ℝ n )}.