  By means of analytical and numerical methods, we address the modulational
instability (MI) in chiral condensates governed by the Gross-Pitaevskiiequation
including the current nonlinearity. The analysis shows that this nonlinearity
partly suppresses off the MI driven by the cubic self-focusing, although the
current nonlinearity is not represented in the system's energy (although it
modifies the momentum), hence it may be considered as zero-energy nonlinearity.
Direct simulations demonstrate generation of trains of stochastically
interacting chiral solitons by MI. In the ring-shaped setup, the MI creates a
single traveling solitary wave. The sign of the current nonlinearity determines
the direction of propagation of the emerging solitons.
