Hokkaido University Preprint Series in Mathematics
Consider the nonlinear wave equation with zero mass and a time-independent otential in three space dimensions. When it comes to the associated Cauchy problem, it s already known that short-range potentials do not a®ect the existence of small-amplitude olutions. In this paper, we focus on the associated scattering problem and we show that he situation is quite di®erent there. In particular, we show that even arbitrarily small and apidly decaying potentials may a®ect the asymptotic behavior of solutions.