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We present a new class of electrostatics problems that are exactly solvable by adding finitely many image charges. Given a charge at some location inside a cavity bounded by up to four conducting grounded segments of spheres: if the spheres have a symmetry derived via a stereographic projection from a 4D finite reflection group, then this is a solvable generalization of the familiar problem of a charge inside a spherical cavity. There are 19 three-parametric families of finite groups formed by
Solitons are non-dispersive wave solutions that arise in a diverse range of nonlinear systems, stablised by a focussing or defocussing nonlinearity. First observed in shallow water, solitons have subsequently been studied in many other fields includi
Strongly interacting particles in one dimension subject to external confinement have become a topic of considerable interest due to recent experimental advances and the development of new theoretical methods to attack such systems. In the case of equ
The accurate modeling of the dielectric properties of water is crucial for many applications in physics, computational chemistry and molecular biology. This becomes possible in the framework of nonlocal electrostatics, for which we propose a novel fo
We study quench dynamics and equilibration in one-dimensional quantum hydrodynamics, which provides effective descriptions of the density and velocity fields in gapless quantum gases. We show that the information content of the large time steady stat
We report the observation of quantum reflection from a narrow, attractive, potential using bright solitary matter-waves formed from a 85Rb Bose-Einstein condensate. We create narrow potentials using a tightly focused, red-detuned laser beam, and obse