Inverse Scattering and Integrability in Multidimensions

This is the authors' abstract. We don't add key points for this paper.

The characterization problem of the inverse data T associated with the inverse scattering for N hyperbolic equations in $n+1$ dimensions, $n>1$, is explicitly solved. A simple relationship is found between T and the scattering amplitude S; if $N=3$, $T=S$. The potential can be reconstructed by just the solving of two hyperbolic equations in two dimensions. The N wave interaction equations are reduced from $n+1$ to two spatial dimensions.