PEAK Staff Profile

Ralph Willox,
Professor – Environmental Sciences



Prof. Willox obtained his Doctorate in Physics in 1993 from the Free University of Brussels (VUB). While still a postdoc his interest in the theory of integrable systems led him to the Graduate School of Mathematical Sciences of the University of Tokyo, one of the leading centers in the world in research in integrable systems, where he was appointed in 2003.

Research Interests

Integrable systems appear in every imaginable field of physics, as idealized systems that enjoy the fullest set of symmetries allowed by theory. They are important not only because they allow for exact calculations (as opposed to approximations) of the quantities that appear in a physical theory, but also because they possess extraordinarily beautiful mathematical properties. This explains why research in integrable systems has been at the crossroads of theoretical physics and pure mathematics for nearly a century and a half.
A particularly interesting problem is how to obtain discrete systems (systems of nonlinear recursion relations or equations defined on lattices) that enjoy properties similar to those found in integrable systems that live in the continuous world (continuous in space and time).

As a spin-off of his research in discrete integrable systems, Prof. Willox is also interested in applying some of the techniques and ideas that he has developed in that domain, to the problem of discretising non-integrable models that appear in epidemiology, ecology or population dynamics, in such a way that their discrete versions preserve the crucial features (solutions, conserved quantities, symmetries etc.) of those models.

Selected Publications

T. Mase et al., “Singularity confinement as an integrability criterion”, J. Phys. A 52 (2019) 205201 [29pp].

J. Nimmo et al., “Darboux dressing and undressing for the ultradiscrete KdV equation”, J. Phys. A 52 (2019) 445201 [36pp].

S. Colin et al., “Can quantum systems succumb to their own (gravitational) attraction?”, Class. Quantum Gravity 31 (2014) 245003 [54pp].

S. Kakei et al., “Yang-Baxter maps and the discrete KP hierarchy”, Glasgow Math. J. 51A (2009) 107-119.

R. Willox et al., “Epidemic dynamics: discrete-time and cellular automaton models”, Physica A 328 (2003) 13-22.

R. Willox et al., "Darboux and binary Darboux transformations for the nonautonomous discrete KP equation", J. Math. Phys. 38 (1997) 6455–6469.

J. Nimmo & R. Willox, “Darboux transformations for the two-dimensional Toda system”, Proc. Royal Soc. London A 453 (1997) 2497-2525.