Linear superposition of Wronskian rational solutions to the KdV equation

A linear superposition is studied for Wronskian rational solutions to the KdV equation, which include rogue wave solutions. It is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear KdV equation. It is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions.