  We study the collisionless dynamics of two classes of nonintegrable pairing
models. One is a BCS model with separable energy-dependent interactions, the
other - a 2D topological superconductor with spin-orbit coupling and a
band-splitting external field. The long-time quantum quench dynamics at
integrable points of these models are well understood. Namely, the squared
magnitude of the time-dependent order parameter $\Delta(t)$ can either vanish
(Phase I), reach a nonzero constant (Phase II), or periodically oscillate as an
elliptic function (Phase III). We demonstrate that nonintegrable models too
exhibit some or all of these nonequilibrium phases. Remarkably, elliptic
periodic oscillations persist, even though both their amplitude and functional
form change drastically with integrability breaking. Striking new phenomena
accompany loss of integrability. First, an extremely long time scale emerges in
the relaxation to Phase III, such that short-time numerical simulations risk
erroneously classifying the asymptotic state. This time scale diverges near
integrable points. Second, an entirely new Phase IV of quasiperiodic
oscillations of $|\Delta|$ emerges in the quantum quench phase diagrams of
nonintegrable pairing models. As integrability techniques do not apply for the
models we study, we develop the concept of asymptotic self-consistency and a
linear stability analysis of the asymptotic phases. With the help of these new
tools, we determine the phase boundaries, characterize the asymptotic state,
and clarify the physical meaning of the quantum quench phase diagrams of BCS
superconductors. We also propose an explanation of these diagrams in terms of
bifurcation theory.
