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Multidimensional Inverse Scattering for the Nonlinear Klein–Gordon Equation with a Potential

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In this paper, we solve the multidimensional inverse scattering problem for the nonlinear Klein–Gordon equation on Rn,n2:2∂t2 u(x,t)-Δu(x,t)+u(x,t)+V0(x)u(x,t)+∑j=1∞ Vj(x)∣u∣2(j0+j)u(x,t) =0.We prove that the small-amplitude limit of the scattering operator determines uniquely all the Vj,j=0,1,…. Our proof gives, as well, a method for the reconstruction of the Vj,j=0,1,…. © 2002 Elsevier Science (USA).

Keywords: Inverse scattering; nonlinear equations.

Document Type: Research Article

Affiliations: Universidad Nacional Autónoma de México, Apartado Postal 20-726, México, DF, 01000, Mexico

Publication date: September 1, 2002

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