  Rational solutions of the fourth order analogue to the Painlev'e equations
are classified. Special polynomials associated with the rational solutions are
introduced. The structure of the polynomials is found. Formulas for their
coefficients and degrees are derived. It is shown that special solutions of the
Fordy - Gibbons, the Caudrey - Dodd - Gibbon and the Kaup - Kupershmidt
equations can be expressed through solutions of the equation studied.
