We examine the stability and dynamics of a family of crossed dark solitons ina harmonically confined Bose-Einstein condensate in two dimensions. Working ina regime where the fundamental snake instability is suppressed, we show theexistence of an instability which leads to an interesting collapse and revivalof the initial state for the fundamental case of two crossed solitons. Theinstability originates from the singular point where the solitons cross, and wecharacterise it by examining the Bogoliubov spectrum. Finally, we extend thetreatment to systems of higher symmetry.
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