Ricardo Weder
Inverse Scattering on the Line for the Nonlinear Klein-Gordon Equation with a Potential
(52K, Latex)

ABSTRACT.  In this paper we obtain a Lp-Lp' estimate for the Klein-Gordon equation 
with a potential on the line. This result follows from previuosly known 
estimates in the case without potential and from the continuity on the 
Sobolev spaces of the Schroedinger wave operators that we proved in a previous paper. Using this estimate we construct the scattering operator for the nonlinear Klein-Gordon equation with a potential. 
Moreover, we prove that the small amplitude scattering operator 
uniquely determines both, the potential and the nonlinearity. Our proof 
gives also a method for the reconstruction of the potential and of the nonlinearity.