Dynamical systems with independent (continuous or discrete) time variable t and phase
space variable x are called reversible if they are invariant under the combination {t→−t, x→Gx} …

Some simple solutions of discrete soliton equations are shown to satisfy 2D mappings. We
show that these belong to a recently introduced 18-parameter family of integrable reversible …

I thought that instead of the great number of precepts of which logic is composed, I would
have enough with the four following ones, provided that I made a firm and unalterable …

This paper discusses the discrete analogue of the gradient of a function and shows how
discrete gradients can be used in the numerical integration of ordinary differential equations (…

A new class of energy-preserving numerical integration methods Page 1 Journal of Physics A:
Mathematical and Theoretical A new class of energy-preserving numerical integration methods …

Eigenspectra of the critical quantum Ashkin-Teller and Potts chains with free boundaries can
be obtained from that of the XXZ chain with free boundaries and a complex surface field. By …

We report an 18-parameter family of integrable reversible mappings of the plane. These
mappings are shown to occur in soliton theory and in statistical mechanics. We conjecture that …

We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs)
with constant symplectic structure, while preserving their energy exactly. The same method…

Starting from the linear integral equation for the solutions of the Korteweg-de Vries (KdV)
equation, we obtain the direct linearization of a general nonlinear difference-difference equation…

Geometric integration is the numerical integration of a differential equation, while preserving
one or more of its' geometric'properties exactly, ie to within round-off error. Many of these …