Special polynomials associated with the fourth order analogue to the Painlev'e equations
Abstract
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.
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