99-325 Ricardo Weder

Inverse Scattering on the Line for the Nonlinear Klein-Gordon Equation with a Potential (52K, Latex) Sep 6, 99

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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.

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