  We study both analytically and numerically the nonlinear stage of the
instability of one-dimensional solitons in a small vicinity of the transition
point from supercritical to subcritical bifurcations in the framework of the
generalized nonlinear Schr\"{o}dinger equation. It is shown that near the
collapsing time the pulse amplitude and its width demonstrate the self-similar
behavior with a small asymmetry at the pulse tails due to self-steepening. This
theory is applied to both solitary interfacial deep-water waves and envelope
water waves with a finite depth and short optical pulses in fibers as well.
