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A reduction of the resonant three-wave interaction to the generic sixth Painleve' equation

Robert Conte·A. Michel Grundland·Micheline Musette
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Abstract

Among the reductions of the resonant three-wave interaction system to six-dimensional differential systems, one of them has been specifically mentioned as being linked to the generic sixth Painleve' equation P6. We derive this link explicitly, and we establish the connection to a three-degree of freedom Hamiltonian previously considered for P6.

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Robert Conte, A. Michel Grundland, Micheline Musette. 2006-04-06. A reduction of the resonant three-wave interaction to the generic sixth Painleve' equation. https://doi.org/10.1088/0305-4470%2F39%2F39%2Fs07

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