A cubic Hamiltonian system with meromorphic solutions

Thomas Kecker

doi:10.1007/s40315-015-0147-6

A cubic Hamiltonian system with meromorphic solutions

Thomas Kecker

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Abstract

A Hamiltonian system in two dependent variables is presented with properties analogous to the Hamiltonian systems associated with the six Painlevé equations. Its solutions are meromorphic functions in the complex plane having only simple poles with three possible residues given by the third roots of unity. Like the Painlevé equations P_I - P_VI the system has families of rational solutions that can be obtained by applying Bäcklund transformations to certain seed solutions.

Original language	English
Pages (from-to)	307-317
Journal	Computational Methods and Function Theory
Volume	16
Issue number	2
Early online date	27 Oct 2015
DOIs	https://doi.org/10.1007/s40315-015-0147-6
Publication status	Published - Jun 2016

Keywords

Hamiltonian system
meromorphic solution
Painleve equations
Bäcklund transformation

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10.1007/s40315-015-0147-6

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The final publication is available at Springer via http://dx.doi.org/10.1007/s40315-015-0147-6.
Accepted author manuscript (Post-print), 262 KB

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AB - A Hamiltonian system in two dependent variables is presented with properties analogous to the Hamiltonian systems associated with the six Painlevé equations. Its solutions are meromorphic functions in the complex plane having only simple poles with three possible residues given by the third roots of unity. Like the Painlevé equations PI - PVI the system has families of rational solutions that can be obtained by applying Bäcklund transformations to certain seed solutions.

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KW - meromorphic solution

KW - Painleve equations

KW - Bäcklund transformation

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JO - Computational Methods and Function Theory

JF - Computational Methods and Function Theory

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A cubic Hamiltonian system with meromorphic solutions

Abstract

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