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Bifurcations of Solitary Waves

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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Main Authors: Kuznetsov, E.A., Agafontsev, D.S., Dias, F.
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2008
Series:Журнал математической физики, анализа, геометрии
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/106521
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spelling irk-123456789-1065212016-09-30T03:03:05Z Bifurcations of Solitary Waves Kuznetsov, E.A. Agafontsev, D.S. Dias, F. 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. 2008 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/106521 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author Kuznetsov, E.A.
Agafontsev, D.S.
Dias, F.
spellingShingle Kuznetsov, E.A.
Agafontsev, D.S.
Dias, F.
Bifurcations of Solitary Waves
Журнал математической физики, анализа, геометрии
author_facet Kuznetsov, E.A.
Agafontsev, D.S.
Dias, F.
author_sort Kuznetsov, E.A.
title Bifurcations of Solitary Waves
title_short Bifurcations of Solitary Waves
title_full Bifurcations of Solitary Waves
title_fullStr Bifurcations of Solitary Waves
title_full_unstemmed Bifurcations of Solitary Waves
title_sort bifurcations of solitary waves
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate 2008
url http://dspace.nbuv.gov.ua/handle/123456789/106521
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.
series Журнал математической физики, анализа, геометрии
work_keys_str_mv AT kuznetsovea bifurcationsofsolitarywaves
AT agafontsevds bifurcationsofsolitarywaves
AT diasf bifurcationsofsolitarywaves
first_indexed 2023-10-18T20:13:08Z
last_indexed 2023-10-18T20:13:08Z
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