- PII
- S30345006S0320791925010024-1
- DOI
- 10.7868/S3034500625010024
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 71 / Issue number 1
- Pages
- 16-26
- Abstract
- Using numerical modeling methods, the processes of generation and propagation of nonlinear periodic waves in a deformable medium modeled by various chains of active Morse–van der Pol particles were studied. In a wide range of chain lengths, the intervals of change in wave periods are determined. It is shown that in short chains the conservative Morse forces are much greater than the spatially dependent forces of active friction, as a result of which the wave process occurs according to a conservative scenario. In long chains, the process of transformation of a nonlinear periodic wave into a dissipative soliton, the minimum speed of which corresponds to the maximum value of the period, has been revealed. It has been established that the dependence of the minimum period on the number of particles in the chain is almost linear. The instability of the propagation of initial disturbances consisting of several previously identified identical periodic solutions is demonstrated.
- Keywords
- нелинейная деформируемая среда цепочки активных частиц Морзе–ван дер Поля периодические волны диссипативный солитон
- Date of publication
- 01.01.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 46
References
- 1. Бобровницкий Ю.И. Модели и общие волновые свойства двумерных акустических метаматериалов и сред // Акуст. журн. 2015. Т. 61. № 3. C. 283–294.
- 2. Bochkarev A.V., Zemlyanukhin A.I. Regular dynamics of active particles in the Van der Pol–Morse chain // Nonlinear Dynamics. 2021 V. 104. P. 4163–4180. https://doi.org/10.1007/s11071-021-06579-w
- 3. Гольдштейн М.Н. Механические свойства грунтов. М.: Изд. лит. по строительству, 1971. 368 с.
- 4. Das B.M., Ramana G.V. Principles of soil dynamics. Cengage learning. 2-nd ed. 2011. 556 p.
- 5. Mavko G., Mukeji T., Dvorkin J. The Rock Physics Handbook. Tools For Seismic Analysis in Porous Media. Cambridge University Press. MA. 2-nd ed. 2009. 524 p.
- 6. Бахолдин Б.В., Ястребов П.И. Дискретная модель песчаных и глинистых грунтов // Строительство и реконструкция. 2015. № 3. С. 4–11.
- 7. Лебедев А.В., Манаков С.А. Экспериментальное исследование медленной релаксации скорости звука в карбонатной породе // Акуст журн. 2024. Т. 70. № 2. C. 253–272. https://doi.org/10.31857/S0320791924020138
- 8. Заславский Ю.М., Заславский В.Ю. Анализ сейсмических колебаний, возбуждаемых движущимся железнодорожным составом // Вычислительная механика сплошных сред. 2021. Т. 14. № 1. С. 91–101. https://doi.org/10.7242/1999-6691/2021.14.1.8
- 9. Velarde M.G., Chetverikov A.P., Ebeling W., Dmitriev S.V., Lakhno V.D. From solitons to discrete breathers // The European Physical J. B. 2016. V. 89. P. 233.
- 10. Chetverikov A.P., Ebeling W., Velarde M.G. Dissipative solitons and complex currents in active lattices // Int. J. of Bifurcation and Chaos. 2006. V. 16. P. 1613–1632.
- 11. Chetverikov A.P., Sergeev K.S., del Rio E. Dissipative Solitons and Metastable States in a Chain of Active Particles // Int. J. of Bifurcation and Chaos. 2018. V. 28. N 08. P. 1830027.
- 12. Bochkarev A.V., Zemlyanukhin A.I., Chetverikov A.P., Velarde M.G. Single and multi-vertices solitons in lattices of active Morse-van der Pol units // Commun. Nonlinear. Sci. Numer. Simul. 2022. V. 114. Art. no. 106678. https://doi.org/10.1016/j.cnsns.2022.106678
- 13. Ерофеев В.И., Колесов Д.А., Мальханов А.О. Нелинейные локализованные продольные волны в метаматериале, задаваемом как цепочка “масса-в-массе” // Акуст. журн. 2022. Т. 68. № 5. С. 475–478.
- 14. Erofeev V.I., Kazhaev V.V., Pavlov I.S. Inelastic interaction and splitting of strain solitons propagating in a one-dimensional granular medium with internal stress // Advanced Structured Materials. 2016. V. 42. P. 145–162.
- 15. Toda M. Theory of Nonlinear Lattices. Springer-Verlag, 1989.
- 16. Valkering T.P. Periodic permanent waves in an anharmonic chain with nearest-neighbour interaction // 1978 J. Phys. A: Math. Gen. 11 1885.
- 17. Makita P. Periodic and homoclinic travelling waves in infinite lattices // Nonlinear Analysis: Theory, Methods & Amp; Applications. 2011. V. 74. N 6. P. 2071–2086. https://doi.org/10.1016/j.na.2010.11.011
- 18. Rodriguez-Achach M., Perez G. Periodic traveling waves in nonlinear chains // Revista Mexicana de Fisica. 1996. V. 42. N 5. P. 878-896.
- 19. Nesterenko V.F., Herbold E.B. Periodic waves in a Hertzian chain // Physics Procedia. 2010. V. 3. P. 457–463.
- 20. Betti M., Pelinovsky D.E. Periodic Travelling Waves in Dimer Granular Chains // J. of Nonlinear Science. 2013. V. 23. P. 689–711.
- 21. Chen J., Pelinovsky D.E. Periodic waves in the discrete mKdV equation: Modulational instability and rogue waves // Physica D. 2023. V. 445. 133652.
- 22. Arioli G., Gazzola F. Periodic motion of an infinite lattice of particles with nearest neighbor interaction // Nonlin. Anal. 1996. V. 26. N. 6. P. 1103–1114.
- 23. Pankov A. Traveling Waves and Periodic Oscillations in Fermi-Pasta-Ulam Lattices. Imperial College Press, London—Singapore, 2005.
- 24. Землянухин А.И., Бочкарев А.В., Павлов И.С. Уединенные волны в цепочке Морзе–ван дер Поля с нелокальными связями между частицами // Изв. ВУЗов: Радиофизика. 2024. Т. 67. № 6. С. 532–544.
