2 research outputs found
A q-analogue of gl_3 hierarchy and q-Painleve VI
A q-analogue of the gl_3 Drinfel'd-Sokolov hierarchy is proposed as a
reduction of the q-KP hierarchy. Applying a similarity reduction and a
q-Laplace transformation to the hierarchy, one can obtain the q-Painleve VI
equation proposed by Jimbo and Sakai.Comment: 14 pages, IOP style, to appear in J. Phys. A Special issue "One
hundred years of Painleve VI
A reduction of the resonant three-wave interaction to the generic sixth Painleve' equation
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.Comment: 13 pages, 0 figure, J. Phys. A Special issue "One hundred years of
Painleve' VI