D.H. de Vries, R.D.H. Wallis de Vries, Een Amsterdamse koopman in de Molukken, 1883-1901, R. Wallis de Vries, ed.

Hugo De Vries

Modal De Vries Algebras

We introduce modal de Vries algebras and develop a duality between the category of modal de Vries algebras and the category of coalgebras for the Vietoris functor on compact Hausdorff spaces. This duality serves as a common generalization of de Vries duality between de Vries algebras and compact Hausdorff spaces, and the duality between modal algebras and modal spaces.

Coupled Korteweg-de Vries equations

When a system supports two distinct long-wave modes with nearly coincident phase speeds, the weakly nonlinear and linear dispersion unfolding generically leads to two coupled Korteweg-de Vries equations. In this paper, we review the derivation of such systems in stratified fluids, extending previous studies by allowing for background shear flows. Coupled Korteweg-de Vries systems have very rich...

Kinematic Spaces and De Vries Algebras: towards Possible Physical Meaning of De Vries Algebras

Traditionally, in physics, space-times are described by (pseudo-)Riemann spaces, i.e., by smooth manifolds with a tensor metric field. However, in several physically interesting situations smoothness is violated: near the Big Bang, at the black holes, and on the microlevel, when we take into account quantum effects. In all these situations, what remains is causality – an ordering relation. To d...

Numerical inverse scattering for the Korteweg–de Vries and modified Korteweg–de Vries equations

Recent advances in the numerical solution of Riemann–Hilbert problems allow for the implementation of a Cauchy initial value problem solver for the Korteweg–de Vries equation (KdV) and the defocusing modified Korteweg–de Vries equation (mKdV), without any boundary approximation. Borrowing ideas from the method of nonlinear steepest descent, this method is demonstrated to be asymptotically accur...