Нелинейные динамические процессы, описываемые обобщенным уравнением Курамото–Сивашинского в переменных бегущей волны
https://doi.org/10.56304/S2304487X20020091
Аннотация
Ключевые слова
Об авторах
С. Ф. Лаврова
Национальный исследовательский ядерный университет “МИФИ”
Россия
Россия
115409
Москва
Н. А. Кудряшов
Национальный исследовательский ядерный университет “МИФИ”
Россия
Россия
115409
Москва
Список литературы
1. Kuramoto Yoshiki, Toshio Tsuzuki. Persistent propagation of concentration waves in dissipative media far from thermal equilibrium // Progress of theoretical physics. 1976. V. 55. № 2. P. 356–369.
2. Sivashinsky G. I. Nonlinear analysis of hydrodynamic instability in laminar flames – I. Derivation of basic equations // Acta astronautica. 1977. V. 4. P. 1177–1206.
3. Michelson D. M., Sivashinsky G. I. Nonlinear analysis of hydrodynamic instability in laminar flames – II. Numerical experiments // Acta astronautica. 1977. V. 4. № 11–12. P. 1207–1221.
4. Sivashinsky G. I. On flame propagation under conditions of stoichiometry // SIAM Journal on Applied Mathematics. 1980. V. 39. № 1. P. 67–82.
5. Tsvelodub O. Yu. Stationary travelling waves on a film flowing down an inclined plane // Fluid Dynamics. 1980. V. 15. № 4. P. 591–594.
6. Shlang T., Sivashinsky G. I. Irregular flow of a liquid film down a vertical column // Journal de Physique. 1982. V. 43. № 3. P. 459–466.
7. Kuramoto Yoshiki. Diffusion-induced chaos in reaction systems // Progress of Theoretical Physics Supplement. 1978. V. 64. P. 346–367.
8. Sivashinsky G. I. Large cells in nonlinear Marangoni convection // Physica D: Nonlinear Phenomena. 1982. V. 4. №. 2. P. 227–235.
9. Kudryashov N. A. Exact solutions of the generalized Kuramoto-Sivashinsky equation // Physics Letters A. 1990. V. 147. № 5–6. P. 287–291.
10. Michelson D. Steady solutions of the Kuramoto-Sivashinsky equation // Physica D: Nonlinear Phenomena. 1986. V. 19. № 1. P. 89–111.
11. Kudryashov N. A. Solitary and periodic solutions of the generalized Kuramoto-Sivashinsky equation. 2011. arXiv preprint arXiv: 1112.5707.
12. Conte R., Micheline M. Painleve analysis and Backlund transformation in the Kuramoto-Sivashinsky equation // Journal of Physics A: Mathematical and General. 1989. V. 22. № 2. P. 169.
13. Hyman J. M., Nicolaenko B. The Kuramoto-Sivashinsky equation: a bridge between PDE’s and dynamical systems // Physica D: Nonlinear Phenomena. 1986. V. 18. № 1–3. P. 113–126.
14. Nicolaenko B., Scheurer B., Temam R. Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors // Physica D: Nonlinear Phenomena. 1985. V. 16. № 2. P. 155–183.
15. Manneville P. Liapounov exponents for the Kuramoto-Sivashinsky model. Macroscopic Modelling of Turbulent Flows. Springer, Berlin, Heidelberg, 1985. P. 319–326.
16. Brummitt Ch. D., Sprott J. C. A search for the simplest chaotic partial differential equation // Physics Letters A. 2009. V. 373. № 31. P. 2717–2721.
17. Kudryashov N. A., Sinel’shchikov D. I., Chernyavsky I. L. Nonlinear evolution equations for description of perturbations in a viscoelastic tube // Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]. 2008. V. 4. № 1. P. 69–86.
18. Benettin G. et al. Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Part 1: Theory // Meccanica. 1980. V. 15. № 1. P. 9–20.
19. Sprott J. C. Elegant chaos: algebraically simple chaotic flows. World Scientific, 2010.
20. Lakshmanan Muthusamy, Shanmuganathan Rajaseekar. Nonlinear dynamics: integrability, chaos and patterns. Springer Science & Business Media, 2012.
Рецензия
Для цитирования:
Лаврова С.Ф., Кудряшов Н.А. Нелинейные динамические процессы, описываемые обобщенным уравнением Курамото–Сивашинского в переменных бегущей волны. Вестник НИЯУ МИФИ. 2020;9(2):129-138. https://doi.org/10.56304/S2304487X20020091
For citation:
Lavrova S.F., Kudryashov N.A. Nonlinear Dynamical Processes Described by the Traveling Wave Reduction of the Generalized Kuramoto–Sivashinsky Equation. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2020;9(2):129-138. (In Russ.) https://doi.org/10.56304/S2304487X20020091
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