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Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension \(n\geq{}2\). (English) Zbl 0776.35070
The authors consider the scattering problem for the nonlinear Schrödinger (NLS) equation \[ i\partial_ tu=-(1/2)\Delta u+f(u), \] in space dimension \(n\geq 2\). The nonlinear interaction term is \(f(u)=\lambda| u|^{p-1}u\) with \(p-1=2/n\) in the NLS case and \(f(u)=\lambda(| x|^{-1}*| u|^ 2)u\) in the Hartree case with Coulomb potential \(V(x)=\lambda| x|^{-1}\).
They prove the existence of modified wave operators in the \(L^ 2\) sense on a dense set of small and sufficiently regular asymptotic states.
Reviewer: A.Tsutsumi (Sakai)

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
35P25 Scattering theory for PDEs
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