  Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is
shown that periodically modulating the transverse confinement, and thus the
nonlinear interactions in the BEC, excites small amplitude longitudinal
oscillations through a parametric resonance. It is also demonstrated that even
without the presence of a continuous drive, an initial transverse breathing
mode excitation of the condensate leads to spontaneous pattern formation in the
longitudinal direction. Finally, the effects of strongly driving the transverse
breathing mode with large amplitude are investigated. In this case,
impact-oscillator behavior and intriguing nonlinear dynamics, including the
gradual emergence of multiple longitudinal modes, are observed.
