Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear Systems

• Дата: 2006
• Автори: Charkina, O.V., Bogdan, M.M.
• 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
• 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.

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.