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arXiv · 0805.1620

Collapse of solitary waves near transition from supercritical to subcritical bifurcations

D. S. Agafontsev·F. Dias·E. A. Kuznetsov
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Abstract

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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D. S. Agafontsev, F. Dias, E. A. Kuznetsov. 2008-05-12. Collapse of solitary waves near transition from supercritical to subcritical bifurcations. https://doi.org/10.1134/s0021364008120047

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