Rational solutions of the fourth and fifth Painlevé hierarchies

Details Rational solutions of the fourth and fifth Painlevé hierarchies Rational solutions of the fourth and fifth Painlevé hierarchies

2011-10-14

arxiv.org/abs/1110.3132v1

Mathematics

Classical Analysis and ODEs

Abstract of the FASDE-2011 conference talk

Scientific paper

We will consider four hierarchies of higher order analogues of the fourth (P4) and fifth (P5) Painleve equations. The necessary and sufficient conditions for having rational solutions will be presented. Further we well consider two more hierarchies of the (P4). We well show that both of them admit the solution in the form of $1/x$. The last result shows that all the considered P4-hierarchies have the common property: they assume the solution $1/x$ as also the original P4 does.

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