Abstract: We analyze the shape and stability of localized states in nonlinear cubic media with space-dependent potentials modeling an inhomogeneity. By means of a static variational approach, we describe the ground states and vortexlike stationary solutions, either in dilute atom gases-or in optical cavities, with an emphasis on parabolic-type potentials. First, we determine the existence conditions for soliton and vortex structures for both focusing and defocusing nonlinearity. It is shown that, even for, a defocusing medium, soliton modes can exist with a confining potential. Second, step potentials and boundedness effects in hollow capillaries are investigated, which both proceed from a similar analysis. Finally, we discuss applications of this procedure to charged vortices in dilute quantum gases and to Bose-Einstein condensates trapped in the presence of a light-induced Gaussian barrier.

Keywords: bose-einstein condensate; self-phase modulation; attractive interactions; dissipative dynamics; stability-criterion; angular-momentum; vortex formation; spatial soliton; trapped beams; dark solitons

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