  We consider a basic $d$-adic model for the scattering transform on the line.
We prove $L^2$ bounds for this scattering transform and a weak $L^2$ bound for
a Carleson type maximal operator. The latter implies boundedness of $d$-adic
models of generalized eigenfunctions of Dirac type operators with potential in
$L^2(R)$. We show that this result cannot be obtained by estimating the terms
in the natural multilinear expansion of the scattering transform.
