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періодичних видань НАН України
Bifurcations of Solitary Waves
Репозиторій DSpace/Manakin
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Bifurcations of Solitary Waves
Посилання:
Bifurcations of Solitary Waves / E.A. Kuznetsov, D.S. Agafontsev, F. Dias // Журнал математической физики, анализа, геометрии. — 2008. — Т. 4, № 4. — С. 529-550. — Бібліогр.: 42 назв. — англ.
Підтримка:
The authors thank A.I. Dyachenko for valuable discussions concerning the numerical simulations. We acknowledge support from CNRS under the framework of PICS No. 4251 and RFBR under Grant 07-01-92165. The work of DA and EK was also supported by RFBR (Grant 06-01-00665), the Program of RAS "Fundamental problems in nonlinear dynamics" and Grant NSh 7550.2006.2.
Дата:
2008
Переглядів:
743
Завантажень:
311
Анотація:
The paper provides a brief review of the recent results devoted to bifurcations of solitary waves. The main attention is paid to the universality of soliton behavior and stability of solitons while approaching supercritical bifurcations. Near the transition point from supercritical to subcritical bifurcations, the stability of two families of solitons is studied in the frame-work of the generalized nonlinear Schrodinger equation. It is shown that one-dimensional solitons corresponding to the family of supercritical bifurcations are stable in the Lyapunov sense. The solitons from the subcritical bifurcation branch are unstable. The development of this instability results in the collapse of solitons. Near the time of collapse, the pulse amplitude and its width exhibit a self-similar behavior with a small asymmetry in the pulse tails due to self-steepening.
