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Hyperelliptic Integrable Systems on K3 and Rational Surfaces
Kanehisa Takasaki
We show several examples of integrable systems related to special K3 and rational surfaces (e.g., an elliptic K3 surface, a K3 surface given by a double covering of the projective…
Anti-self-dual Yang-Mills equations on noncommutative spacetime
Kanehisa Takasaki
By replacing the ordinary product with the so called -product, one can construct an analogue of the anti-self-dual Yang-Mills (ASDYM) equations on the noncommutative $\bbR^4…
Toroidal Lie algebras and Bogoyavlensky's 2+1-dimensional equation
T. Ikeda, K. Takasaki
We introduce an extension of the \ell-reduced KP hierarchy, which we call the \ell-Bogoyavlensky hierarchy. Bogoyavlensky's 2+1-dimensional extension of the KdV equation is the low…
Painleve-Calogero Correspondence Revisited
Kanehisa Takasaki
We extend the work of Fuchs, Painlevé and Manin on a Calogero-like expression of the sixth Painlevé equation (the ``Painlevé-Calogero correspondence'') to the other five Painlevé e…