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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:nlin/0302012 (nlin)
[Submitted on 6 Feb 2003 (v1), last revised 14 Apr 2003 (this version, v2)]

Title:Painleve equations from Darboux chains - Part 1: P3-P5

Authors:Ralph Willox, Jarmo Hietarinta
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Abstract: We show that the Painleve equations P3-P5 can be derived (in a unified way) from a periodic sequence of Darboux transformations for a Schrodinger problem with quadratic eigenvalue dependency. The general problem naturally divides into three different branches, each described by an infinite chain of equations. The Painleve equations are obtained by closing the chain periodically at the lowest nontrivial level(s). The chains provide ``symmetric forms'' for the Painleve equations, from which Hirota bilinear forms and Lax pairs are derived. In this paper (Part 1) we analyze in detail the cases P3-P5, while P6 will be studied in Part 2.
Comments: 23 pages, 1 reference added + minor changes
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:nlin/0302012 [nlin.SI]
  (or arXiv:nlin/0302012v2 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.nlin/0302012
Related DOI: https://doi.org/10.1088/0305-4470/36/42/014

Submission history

From: Jarmo Hietarinta [view email]
[v1] Thu, 6 Feb 2003 13:43:40 UTC (21 KB)
[v2] Mon, 14 Apr 2003 09:28:03 UTC (22 KB)
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