303 citations · 612 across the 16 of their papers we have counts for
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Three classes of quadratic vector fields for which the Kahan discretization is the root of a generalised Manin transformation
Peter H. van der Kamp, Elena Celledoni, Robert I. McLachlan +3
We apply Kahan's discretisation method to three classes of 2-dimensional quadratic vector fields with quadratic, resp cubic, resp quartic Hamiltonians. We show that the maps obtain…
Integrability properties of Kahan's method
Elena Celledoni, Robert I McLachlan, David I McLaren +2
We present several novel examples of integrable quadratic vector fields for which Kahan's discretization method preserves integrability. Our examples include generalized Suslov and…
Construction of Integrals of Higher-Order Mappings
Ken-ichi Maruno, G. R. W. Quispel
We find that certain higher-order mappings arise as reductions of the integrable discrete A-type KP (AKP) and B-type KP (BKP) equations. We find conservation laws for the AKP and B…