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

This book on integrable systems and symmetries presents new results on applications of
symmetries and integrability techniques to the case of equations defined on the lattice. This …

We present all real quantum mechanical potentials in a two-dimensional Euclidean space
that have the following properties: 1. They allow separation of variables of the Schrödinger …

The general description of superintegrable systems with one polynomial integral of order N
in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean plane …

The superintegrability of several Hamiltonian systems defined on three-dimensional
configuration spaces of constant curvature is studied. We first analyze the properties of the …

We consider superintegrability in classical mechanics in the presence of magnetic fields. We
focus on three-dimensional systems which are separable in Cartesian coordinates. We …

A study is presented of two-dimensional superintegrable systems separating in Cartesian
coordinates and allowing an integral of motion that is a fourth order polynomial in the …

We study four particular three-dimensional natural Hamiltonian systems defined in
conformally Euclidean spaces. We prove their superintegrability and we obtain, in the four …

Cylindrical type integrable classical systems in a magnetic field - IOPscience This site uses
cookies. By continuing to use this site you agree to our use of cookies. To find out more, see …

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 …