Interaction of Solitons for Sine-Gordon-Type Equations
The subject of our consideration is a family of semilinear wave equations with a small parameter and nonlinearities which provide the existence of kink-type solutions (solitons). Using asymptotic analysis and numerical simulation, we demonstrate that solitons of the same type (kinks or antikinks) in...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/845926 |
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| author | Georgii A. Omel’yanov Israel Segundo-Caballero |
| author_facet | Georgii A. Omel’yanov Israel Segundo-Caballero |
| author_sort | Georgii A. Omel’yanov |
| collection | DOAJ |
| description | The subject of our consideration is a family of semilinear wave equations with a small parameter and nonlinearities which provide the existence of kink-type solutions (solitons). Using asymptotic analysis and numerical simulation, we demonstrate that solitons of the same type (kinks or antikinks) interact in the same manner as for the sine-Gordon equation. However, solitons of the different type preserve the shape after the interaction only in the case of two or three waves, and, moreover, under some additional conditions. |
| format | Article |
| id | doaj-art-3cc2b10409e74c6a9ef09ab1f1efcadc |
| institution | DOAJ |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-3cc2b10409e74c6a9ef09ab1f1efcadc2025-08-20T02:39:11ZengWileyJournal of Mathematics2314-46292314-47852013-01-01201310.1155/2013/845926845926Interaction of Solitons for Sine-Gordon-Type EquationsGeorgii A. Omel’yanov0Israel Segundo-Caballero1Department of Mathematics, University of Sonora, Rosales y Boulevard Encinas s/n, 83000 Hermosillo, MexicoDepartment of Mathematics, University of Sonora, Rosales y Boulevard Encinas s/n, 83000 Hermosillo, MexicoThe subject of our consideration is a family of semilinear wave equations with a small parameter and nonlinearities which provide the existence of kink-type solutions (solitons). Using asymptotic analysis and numerical simulation, we demonstrate that solitons of the same type (kinks or antikinks) interact in the same manner as for the sine-Gordon equation. However, solitons of the different type preserve the shape after the interaction only in the case of two or three waves, and, moreover, under some additional conditions.http://dx.doi.org/10.1155/2013/845926 |
| spellingShingle | Georgii A. Omel’yanov Israel Segundo-Caballero Interaction of Solitons for Sine-Gordon-Type Equations Journal of Mathematics |
| title | Interaction of Solitons for Sine-Gordon-Type Equations |
| title_full | Interaction of Solitons for Sine-Gordon-Type Equations |
| title_fullStr | Interaction of Solitons for Sine-Gordon-Type Equations |
| title_full_unstemmed | Interaction of Solitons for Sine-Gordon-Type Equations |
| title_short | Interaction of Solitons for Sine-Gordon-Type Equations |
| title_sort | interaction of solitons for sine gordon type equations |
| url | http://dx.doi.org/10.1155/2013/845926 |
| work_keys_str_mv | AT georgiiaomelyanov interactionofsolitonsforsinegordontypeequations AT israelsegundocaballero interactionofsolitonsforsinegordontypeequations |