Existence and Uniqueness of Tri-tronquée Solutions of the second Painlevé hierarchy

Details Existence and Uniqueness of Tri-tronquée Solutions of the second Painlevé hierarchy Existence and Uniqueness of Tri-tronquée Solutions of the second Painlevé hierarchy

2002-12-09

arxiv.org/abs/math/0212117v1

Mathematics

Classical Analysis and ODEs

13 pages, Latex

Scientific paper

10.1088/0951-7715/16/2/304

The first five classical Painlev\'e equations are known to have solutions
described by divergent asymptotic power series near infinity. Here we prove
that such solutions also exist for the infinite hierarchy of equations
associated with the second Painlev\'e equation. Moreover we prove that these
are unique in certain sectors near infinity.

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