Kink dynamics of the sine-Gordon equation in a model with three identical attracting or repulsive impurities
Purpose of this work is to use analytical and numerical methods to consider the problem of the structure and dynamics of the kinks in the sine-Gordon model with “impurities” (or spatial inhomogeneity of the periodic potential). Methods. Using the method of collective variables f...
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| Format: | Article |
| Language: | English |
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Saratov State University
2023-11-01
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| Series: | Известия высших учебных заведений: Прикладная нелинейная динамика |
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| Online Access: | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2023/11/and_2024-6_ekomasov-et-al_693-709.pdf |
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| author | Ekomasov, Evgenii G Kudryavtsev, Roman V Samsonov, Kirill Yurievich Nazarov, Vladimir Николаевич Kabanov, Daniil Константинович |
| author_facet | Ekomasov, Evgenii G Kudryavtsev, Roman V Samsonov, Kirill Yurievich Nazarov, Vladimir Николаевич Kabanov, Daniil Константинович |
| author_sort | Ekomasov, Evgenii G |
| collection | DOAJ |
| description | Purpose of this work is to use analytical and numerical methods to consider the problem of the structure and dynamics of the kinks in the sine-Gordon model with “impurities” (or spatial inhomogeneity of the periodic potential). Methods. Using the method of collective variables for the case of three identical point impurities located at the same distance from each other, a system of differential equations is obtained. Resulting system of equations makes it possible to describe the dynamics of the kink taking into account the excitation of localized waves on impurities. To analyze the dynamics of the kink in the case of extended impurities, a numerical finite difference method with an explicit integration scheme was applied. Frequency analysis of kink oscillations and localized waves calculated numerically was performed using a discrete Fourier transform. Results. For the kink dynamics, taking into account the excitation of oscillations in modes, a system of equations for the coordinate of the kink center and the amplitudes of waves localized on impurities is obtained and investigated. Significant differences are observed in the dynamics of the kink when interacting with a repulsive and attractive impurity. The dynamics of the kink in a model with three identical extended impurities, taking into account possible resonant effects, was solved numerically. It is established that the found scenarios of kink dynamics for an extended rectangular impurity are qualitatively similar to the scenarios obtained for a point impurity described using a delta function. All possible scenarios of kink dynamics were determined and described taking into account resonant effects. Conclusion. The analysis of the influence of system parameters and initial conditions on possible scenarios of kink dynamics is carried out. Critical and resonant kink velocities are found as functions of the impurity parameters. |
| first_indexed | 2024-03-09T14:06:24Z |
| format | Article |
| id | doaj.art-f1e3fbb6f1234734bece783892755093 |
| institution | Directory Open Access Journal |
| issn | 0869-6632 2542-1905 |
| language | English |
| last_indexed | 2024-03-09T14:06:24Z |
| publishDate | 2023-11-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия высших учебных заведений: Прикладная нелинейная динамика |
| spelling | doaj.art-f1e3fbb6f1234734bece7838927550932023-11-30T05:01:56ZengSaratov State UniversityИзвестия высших учебных заведений: Прикладная нелинейная динамика0869-66322542-19052023-11-0131669370910.18500/0869-6632-003069Kink dynamics of the sine-Gordon equation in a model with three identical attracting or repulsive impuritiesEkomasov, Evgenii G0Kudryavtsev, Roman V1Samsonov, Kirill Yurievich2Nazarov, Vladimir НиколаевичKabanov, Daniil КонстантиновичBashkir State University, 450076, Russian Federation, Republic of Bashkortostan, Ufa, st. Zaki Validi 32Bashkir State University, 450076, Russian Federation, Republic of Bashkortostan, Ufa, st. Zaki Validi 32University of Tyumen , 6 Volodarskogo Street, 625003 TyumenPurpose of this work is to use analytical and numerical methods to consider the problem of the structure and dynamics of the kinks in the sine-Gordon model with “impurities” (or spatial inhomogeneity of the periodic potential). Methods. Using the method of collective variables for the case of three identical point impurities located at the same distance from each other, a system of differential equations is obtained. Resulting system of equations makes it possible to describe the dynamics of the kink taking into account the excitation of localized waves on impurities. To analyze the dynamics of the kink in the case of extended impurities, a numerical finite difference method with an explicit integration scheme was applied. Frequency analysis of kink oscillations and localized waves calculated numerically was performed using a discrete Fourier transform. Results. For the kink dynamics, taking into account the excitation of oscillations in modes, a system of equations for the coordinate of the kink center and the amplitudes of waves localized on impurities is obtained and investigated. Significant differences are observed in the dynamics of the kink when interacting with a repulsive and attractive impurity. The dynamics of the kink in a model with three identical extended impurities, taking into account possible resonant effects, was solved numerically. It is established that the found scenarios of kink dynamics for an extended rectangular impurity are qualitatively similar to the scenarios obtained for a point impurity described using a delta function. All possible scenarios of kink dynamics were determined and described taking into account resonant effects. Conclusion. The analysis of the influence of system parameters and initial conditions on possible scenarios of kink dynamics is carried out. Critical and resonant kink velocities are found as functions of the impurity parameters.https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2023/11/and_2024-6_ekomasov-et-al_693-709.pdfsine-gordon equationkinksolitonbreathermethod of collective coordinatesimpurity |
| spellingShingle | Ekomasov, Evgenii G Kudryavtsev, Roman V Samsonov, Kirill Yurievich Nazarov, Vladimir Николаевич Kabanov, Daniil Константинович Kink dynamics of the sine-Gordon equation in a model with three identical attracting or repulsive impurities Известия высших учебных заведений: Прикладная нелинейная динамика sine-gordon equation kink soliton breather method of collective coordinates impurity |
| title | Kink dynamics of the sine-Gordon equation in a model with three identical attracting or repulsive impurities |
| title_full | Kink dynamics of the sine-Gordon equation in a model with three identical attracting or repulsive impurities |
| title_fullStr | Kink dynamics of the sine-Gordon equation in a model with three identical attracting or repulsive impurities |
| title_full_unstemmed | Kink dynamics of the sine-Gordon equation in a model with three identical attracting or repulsive impurities |
| title_short | Kink dynamics of the sine-Gordon equation in a model with three identical attracting or repulsive impurities |
| title_sort | kink dynamics of the sine gordon equation in a model with three identical attracting or repulsive impurities |
| topic | sine-gordon equation kink soliton breather method of collective coordinates impurity |
| url | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2023/11/and_2024-6_ekomasov-et-al_693-709.pdf |
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