Long range scattering for the wave-Schrödinger system revisited (Q652497)

The paper is devoted to the theory of scattering for the wave-Schrödinger system \[ \begin{cases} i \partial_{t} u + (1/2) \bigtriangleup u = - A u, \\ \square A = | u |^{2}, \end{cases} \] where \(u\) is considered a complex valued function and \(A\) a real valued function defined in space time \(\mathbb{R}^{3 + 1}, \;\triangle\) is the Laplacian in \(\mathbb{R}^{3}\) and \(\square = \partial_{t}^{2} - \bigtriangleup\) is the d'Alembertian. Namely, for arbitrarily large asymptotic data, the Cauchy problem at infinite initial time, which is the first step in the construction of the wave operators, is investigated. The authors have previously studied this problem in [Ann. Henri Poincaré 3, No. 3, 537--612 (2002; Zbl 1025.35014); ibid. 4, No. 5, 973--999 (2003; Zbl 1106.35097); Dyn. Partial Differ. Equ. 2, No. 2, 101--125 (2005; Zbl 1107.35095)].