Geodesic
Special polynomials and rational solutions of the~hierarchy of the~second Painlev\'e equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 58-67

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We study special polynomials used to represent rational solutions of the hierarchy of the second Painlevé equation. We find several recursion relations satisfied by these polynomials. In particular, we obtain a differential–difference relation that allows finding any polynomial recursively. This relation is an analogue of the Toda chain equations.
Keywords: Painlevé equations, hierarchy of the second Painlevé equation, special polynomial, Toda chain.
Mots-clés : rational solution 
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     author = {M. V. Demina and N. A. Kudryashov},
     title = {Special polynomials and rational solutions of the~hierarchy of the~second {Painlev\'e} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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M. V. Demina; N. A. Kudryashov. Special polynomials and rational solutions of the~hierarchy of the~second Painlev\'e equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 58-67. http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a4/