  Superconducting vortices and phase slips are primary mechanisms of
dissipation in superconducting, superfluid, and cold atom systems. While the
dynamics of vortices is fairly well described, phase slips occurring in
quasi-one dimensional superconducting wires still elude understanding. The main
reason is that phase slips are strongly non-linear time-dependent phenomena
that cannot be cast in terms of small perturbations of the superconducting
state. Here we study phase slips occurring in superconducting weak links.
Thanks to partial suppression of superconductivity in weak links, we employ a
weakly nonlinear approximation for dynamic phase slips. This approximation is
not valid for homogeneous superconducting wires and slabs. Using the numerical
solution of the time-dependent Ginzburg-Landau equation and bifurcation
analysis of stationary solutions, we show that the onset of phase slips occurs
via an infinite period bifurcation, which is manifested in a specific
voltage-current dependence. Our analytical results are in good agreement with
simulations.
