  Motivated by recent efforts to achieve cold fermions pairing near a Feshbach
resonance, we consider the dynamics of formation of the
Bardeen-Cooper-Schrieffer (BCS) state. At times shorter than the quasiparticle
energy relaxation time, after the interaction is turned on, the dynamics of the
system is nondissipative. We show that this collective nonlinear evolution of
the BCS-Bogoliubov amplitudes (u,v) along with the pairing function, is an
integrable dynamical problem, and obtain a family of exact solutions in the
form of single solitons and soliton trains. We interpret the collective
oscillations as Bloch precession of Anderson pseudospins, where each soliton
causes a pseudospin full Rabi rotation. Numerical simulations demonstrate
robustness of the solitons with respect to noise and damping.
