  We show that Faraday patterns can be excited in the weak confinement space of
low-dimensional Bose-Einstein condensates by temporal modulation of the trap
width, or equivalently of the trap frequency Omega_tight, in the tight
confinement space. For slow modulation, as compared with Omega_tight, the
low-dimensional dynamics of the condensate in the weak confinement space is
described by a Gross-Pitaevskii equation with time modulated nonlinearity
coefficient. For increasing modulation frequencies a noticeable reduction of
the pattern formation threshold is observed close to 2*Omega_tight, which is
related to the parametric excitation of the internal breathing mode in the
tight confinement space. These predictions could be relevant for the
experimental excitation of Faraday patterns in Bose-Einstein condensates.

Soft Condensed Matter;Statistical Mechanics