Flavor solitons in dense neutrino gases

We consider a dense neutrino gas in the ``fast-flavor limit'' (vanishing neutrino masses). For the first time, we identify exact solutions of the nonlinear wave equation in the form of solitons. They can propagate with both subluminal or superluminal speed, the latter not violating causality. The soliton with infinite speed is a homogeneous solution and coincides with the usual fast-flavor pendulum except that it swings only once instead of being periodic. The subluminal soliton in the static limit corresponds to a one-swing ``spatial pendulum.'' A necessary condition for such solutions to exist is a ``crossed'' neutrino angle distribution. Based on the Nyquist criterion, we derive a new sufficient condition without solving the dispersion relation. The solitons are very fragile; they are as unstable as the homogeneous neutrino gas alone. Moreover, in the presence of matter, only the solution survives that is homogeneous in a frame comoving with the matter current. Generally, the matter effect cannot be eliminated by transformations in flavor space, but has real physical impact.