Collapse of solitary waves near the transition from supercritical to subcritical bifurcations

The nonlinear stage of the instability of one-dimensional solitons within a small vicinity of the transition point from supercritical to subcritical bifurcations has been studied both analytically and numerically using the generalized nonlinear Schrödinger equation. It is shown that the pulse amplitude and its width near the collapsing time demonstrate a self-similar behavior with a small asymmetry at the pulse tails due to self-steepening. This theory is applied to solitary interfacial deep-water waves, envelope water waves with a finite depth, and short optical pulses in fibers.