Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear Systems
The transition from integrable to non-integrable highly-dispersive nonlinear models is investigated. The sine-Gordon and φ⁴-equations with the additional fourth-order spatial and spatio-temporal derivatives, describing the higher dispersion, and with the terms originated from nonlinear interactions...
Збережено в:
| Дата: | 2006 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2006
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146178 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear Systems / O.V. Charkina, M.M. Bogdan // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 28 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146178 |
|---|---|
| record_format |
dspace |
| fulltext |
|
| spelling |
irk-123456789-1461782019-02-08T01:23:56Z Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear Systems Charkina, O.V. Bogdan, M.M. The transition from integrable to non-integrable highly-dispersive nonlinear models is investigated. The sine-Gordon and φ⁴-equations with the additional fourth-order spatial and spatio-temporal derivatives, describing the higher dispersion, and with the terms originated from nonlinear interactions are studied. The exact static and moving topological kinks and soliton-complex solutions are obtained for a special choice of the equation parameters in the dispersive systems. The problem of spectra of linear excitations of the static kinks is solved completely for the case of the regularized equations with the spatio-temporal derivatives. The frequencies of the internal modes of the kink oscillations are found explicitly for the regularized sine-Gordon and φ⁴-equations. The appearance of the first internal soliton mode is believed to be a criterion of the transition between integrable and non-integrable equations and it is considered as the sufficient condition for the non-trivial (inelastic) interactions of solitons in the systems. 2006 Article Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear Systems / O.V. Charkina, M.M. Bogdan // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 28 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 34A05; 34A34; 35G25 http://dspace.nbuv.gov.ua/handle/123456789/146178 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The transition from integrable to non-integrable highly-dispersive nonlinear models is investigated. The sine-Gordon and φ⁴-equations with the additional fourth-order spatial and spatio-temporal derivatives, describing the higher dispersion, and with the terms originated from nonlinear interactions are studied. The exact static and moving topological kinks and soliton-complex solutions are obtained for a special choice of the equation parameters in the dispersive systems. The problem of spectra of linear excitations of the static kinks is solved completely for the case of the regularized equations with the spatio-temporal derivatives. The frequencies of the internal modes of the kink oscillations are found explicitly for the regularized sine-Gordon and φ⁴-equations. The appearance of the first internal soliton mode is believed to be a criterion of the transition between integrable and non-integrable equations and it is considered as the sufficient condition for the non-trivial (inelastic) interactions of solitons in the systems. |
| format |
Article |
| author |
Charkina, O.V. Bogdan, M.M. |
| spellingShingle |
Charkina, O.V. Bogdan, M.M. Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear Systems Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Charkina, O.V. Bogdan, M.M. |
| author_sort |
Charkina, O.V. |
| title |
Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear Systems |
| title_short |
Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear Systems |
| title_full |
Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear Systems |
| title_fullStr |
Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear Systems |
| title_full_unstemmed |
Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear Systems |
| title_sort |
internal modes of solitons and near-integrable highly-dispersive nonlinear systems |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146178 |
| citation_txt |
Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear Systems / O.V. Charkina, M.M. Bogdan // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 28 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT charkinaov internalmodesofsolitonsandnearintegrablehighlydispersivenonlinearsystems AT bogdanmm internalmodesofsolitonsandnearintegrablehighlydispersivenonlinearsystems |
| first_indexed |
2025-07-10T23:21:21Z |
| last_indexed |
2025-07-10T23:21:21Z |
| _version_ |
1837304048238198784 |