Collapse of solitary waves near transition from supercritical to subcritical bifurcations

D.S. Agafontsev, F. Dias and E.A. Kuznetsov
Arxiv ID: 0805.1620Last updated: 12/9/2022
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.

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