A reduction of the resonant three-wave interaction to the generic sixth Painleve' equation
Robert Conte, A. Michel Grundland, Micheline Musette
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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