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

Abstract

The first five classical Painlevé 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 Painlevé equation. Moreover we prove that these are unique in certain sectors near infinity.

arXiv comment13 pages, Latex

References in corpus (1)

• Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approach

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