00-285 Ricardo Weder

Multidimensional Inverse Scattering for the Nonlinear Klein-Gordon Equation with a Potential (37K, Latex) Jul 7, 00

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Abstract. In this paper we solve the multidimensional inverse scattering problem for the nonlinear Klein-Gordon equation on $\ER^n, n \geq 2$: $$ \frac{\partial^2}{\partial t^2} u(x,t) -\Delta u(x,t)+ u(x,t) + V_0(x) u(x,t) +\sum_{j=1}^{\infty} V_j(x) |u|^{2(j_0+j)} u(x,t)=0. $$ We prove that the small-amplitude limit of the scattering operator determines uniquely all the $V_j, j=0,1, \cdots $. Our proof gives, as well, a method for the reconstruction of the $V_j, j=0,1, \cdots$.

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