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

机译:与四阶模拟相关的特殊多项式   painlev'e方程式

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摘要

Rational solutions of the fourth order analogue to the Painlev'e equationsare classified. Special polynomials associated with the rational solutions areintroduced. The structure of the polynomials is found. Formulas for theircoefficients and degrees are derived. It is shown that special solutions of theFordy - Gibbons, the Caudrey - Dodd - Gibbon and the Kaup - Kupershmidtequations can be expressed through solutions of the equation studied.
机译:对Painlev'e方程的四阶类似物的有理解进行了分类。介绍了与有理解相关的特殊多项式。找到多项式的结构。推导了它们的系数和度的公式。结果表明,可以通过所研究方程的解来表达Fo​​rdy-Gibbons,Caudrey-Dodd-Gibbon和Kaup-Kupershmidt等式的特殊解。

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