Bifurcations of Solitary Waves
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 bi...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2008 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106521 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862724086894952448 |
|---|---|
| author | Kuznetsov, E.A. Agafontsev, D.S. Dias, F. |
| author_facet | Kuznetsov, E.A. Agafontsev, D.S. Dias, F. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | 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.
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| first_indexed | 2025-12-07T18:45:38Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106521 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T18:45:38Z |
| publishDate | 2008 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Kuznetsov, E.A. Agafontsev, D.S. Dias, F. 2016-09-29T20:25:03Z 2016-09-29T20:25:03Z 2008 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. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106521 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. 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. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Bifurcations of Solitary Waves Article published earlier |
| spellingShingle | Bifurcations of Solitary Waves Kuznetsov, E.A. Agafontsev, D.S. Dias, F. |
| title | Bifurcations of Solitary Waves |
| title_full | Bifurcations of Solitary Waves |
| title_fullStr | Bifurcations of Solitary Waves |
| title_full_unstemmed | Bifurcations of Solitary Waves |
| title_short | Bifurcations of Solitary Waves |
| title_sort | bifurcations of solitary waves |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106521 |
| work_keys_str_mv | AT kuznetsovea bifurcationsofsolitarywaves AT agafontsevds bifurcationsofsolitarywaves AT diasf bifurcationsofsolitarywaves |