  We characterize the rational solutions to a KdV-like equation which are
generated from polynomial solutions to the corresponding generalized bilinear
equation. We use a particular class of polynomials satisfying a quadratic
difference equation to obtain that there are no solutions of the bilinear
equation with degree (in the spatial variable) greater than 5. As a byproduct,
we answer positively a conjecture of Yi Zhang and Wen-Xiu Ma about these
solutions.
