CLASS OF NON-LINEAR SCHRODINGER EQUATIONS .2. SCATTERING THEORY, GENERAL-CASE

This is the second of a series of papers devoted to the study of a class of non linear Schrödinger equations of the form i( du dt) = (-Δ + m)u + f(u) in Rn where m is a real constant and f a complex valued non linear function. Here we study the scattering theory for the pair of equations that consists of the previous one and of the equation i( du dt) = (-Δ + m)u for n ≥ 2. Under suitable assumptions of f we prove the existence of the wave operators and asymptotic completeness for a class of repulsive interactions. The assumptions of f that ensure asymptotic completeness cover the case of a single power f(u) = λ | u |p-1u where λ ≥ 0 and (n + 4) n < p < (n + 2) (n - 2). © 1979.