On a class of nonlinear Schrödinger equations. II. Scattering theory, general case


AbstractThis is the second of a series of papers devoted to the study of a class of non linear Schrödinger equations of the form i(dudt) = (−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(dudt) = (−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)

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