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

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

2006-05-16

arxiv.org/abs/nlin/0605034v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages

Scientific paper

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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