Separation of variables methods for solving partial differential equations are of immense
theoretical and practical importance in mathematical physics. They are the most powerful …

Second-order (maximally) superintegrable systems in dimensions two and three are
essentially classified. With increasing dimension, however, the non-linear partial differential …

We review recent results on superintegrable quantum systems in a two-dimensional
Euclidean space with the following properties. They are integrable because they allow the …

Superintegrable systems of 2nd order in 3 dimensions with exactly 3-parameter potentials
are intriguing objects. Next to the nondegenerate 4-parameter potential systems they admit …

Abstract The Bannai–Ito algebra can be defined as the centralizer of the coproduct
embedding of osp (1| 2) in osp (1| 2)⊗ n. It will be shown that it is also the commutant of a …

In recent years, progress toward the classification of superintegrable systems with higher
order integrals of motion has been made. In particular, a complete classification of all exotic …

We reconsider non-degenerate second order superintegrable systems in dimension two as
geometric structures on conformal surfaces. This extends a formalism developed by the …

Superintegrable systems are a class of physical systems which possess more conserved
quantities than their degrees of freedom. The study of these systems has a long history and …

Second-order superintegrable systems in dimensions two and three are essentially
classified. With increasing dimension, however, the non-linear partial differential equations …

In this review we present recent results in the field of analytical contraction of Lie algebra in
two-dimensional hyperbolic space. A complete geometric description for all possible …