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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:nlin/0606040 (nlin)
[Submitted on 14 Jun 2006 (v1), last revised 26 Oct 2006 (this version, v2)]

Title:An integrable hierarchy with a perturbed Henon-Heiles system

Authors:A.N.W. Hone, V.S Novikov, C. Verhoeven
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Abstract: We consider an integrable scalar partial differential equation (PDE) that is second order in time. By rewriting it as a system and applying the Wahlquist-Estabrook prolongation algebra method, we obtain the zero curvature representation of the equation, which leads to a Lax representation in terms of an energy-dependent Schrödinger spectral problem of the type studied by Antonowicz and Fordy. The solutions of this PDE system, and of its associated hierarchy of commuting flows, display weak Painlevé behaviour, i.e. they have algebraic branching. By considering the travelling wave solutions of the next flow in the hierarchy, we find an integrable perturbation of the case (ii) Henon-Heiles system which has the weak Painlevé property. We perform separation of variables for this generalized Henon-Heiles system, and describe the corresponding solutions of the PDE.
Comments: Further comments and references added
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)
Report number: UKC/IMS/06/13
Cite as: arXiv:nlin/0606040 [nlin.SI]
  (or arXiv:nlin/0606040v2 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.nlin/0606040
Journal reference: Inverse Problems 22 (2006) 2001-2020
Related DOI: https://doi.org/10.1088/0266-5611/22/6/006

Submission history

From: Andrew Hone N.W. [view email]
[v1] Wed, 14 Jun 2006 15:20:49 UTC (83 KB)
[v2] Thu, 26 Oct 2006 14:12:42 UTC (84 KB)
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