We report an algorithm of constructing linear and nonlinear potentials in the two-dimensional Gross-Pitaevskii equation subject to given boundary conditions, which allow for exact analytic solutions. The obtained solutions represent superfluid flows in inhomogeneous Bose-Einstein condensates. The method is based on the combination of the similarity reduction of the two-dimensional Gross-Pitaevs...

Collapse of (2+1)-dimensional beams in the inhomogeneous two-dimensional cubic nonlinear Schrödinger equation is analyzed numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams that in a homogeneous medium would collapse may be arrested under certain circumstances.

A fundamental ingredient that controls the kinetics of the two-species annihilation process, A + B → 0, is the rate of reaction in the interfacial region between a domain of A’s and a domain of B’s. A natural way to study this interface is to prepare a system with initially separated components and then monitor the reaction rate as a function of time, as first studied by Gálfi and Rácz [1]. Thi...