Послать статью по эл. почте 
Формальная диагонализация схем Лакса–Дарбу
https://doi.org/10.18255/1818-1015-2015-6-795-817
Аннотация
Об авторе
А. В. МихайловВеликобритания
доктор физико-математических наук, профессор,
University of Leeds, Leeds, LS2 9JT, UK
Список литературы
1. V. B. Matveev, M. A. Salle, Darboux Transformations and Solitons, Springer Series in Nonlinear Dynamics 4, Springer-Verlag, Berlin, 1991.
2. C. Rogers, W. K. Schief, “B¨acklund and Darboux transformations”, Geometry and modern applications in soliton theory, Cambridge Texts in Applied Mathematics, 2002.
3. A. I. Bobenko, Yu. B. Suris, “Integrable systems on quad-graphs”, Int. Math. Res. Notices, 11, 573–611.
4. F. Khanizadeh, A. V. Mikhailov, Jing Ping Wang, “Darboux transformations and recursion operators for differential-difference equations”, Theoretical and Mathematical Physics, 177(3) (2013), 1606–1654.
5. A. V. Mikhailov, G. Papamikos, Jing Ping Wang, “Darboux transformation with dihedral reduction group”, Journal of Mathematical Physics, 55(11) (2014), 113507, arXiv: 1402.5660.
6. W. R. Wasow, Asymptotic expansions of solutions of ordinary differential equations, Pure and applied mathematics, Wiley Interscience Publishes, New York, 1965.
7. V. G. Drinfel’d, V. V. Sokolov, “Lie algebras and equations of Korteweg– de Vries type”, Itogi Nauki i Tekhniki, 24, Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1984, 81–180.
8. A. V. Mikhailov, A. B. Shabat, “Conditions for integrability of systems of two equations of the form ut = A(u)uxx + F(u, ux). I”, Teoret. Mat. Fiz., 62(2) (1985), 163–185.
9. A. V. Mikhailov, “Formal diagonalisation of Darboux transformation and conservation laws of integrable PDEs, PD∆Es and P∆Es”, International Workshop “Geometric Structures in Integrable Systems” (October 30 November 02, 2012, M.V. Lomonosov Moscow State University, Moscow), http://www.mathnet.ru/php/presentation.phtml?option_lang=eng&presentid=5934.
10. A. V. Mikhailov, “Formal diagonalisation of the Lax-Darboux scheme and conservation laws of integrable partial differential, differential-difference and partial difference”, DIS A follow-up meeting (8–12 July 2013, Isaac Newton Institute for Mathematical Sciences), http://www.newton.ac.uk/programmes/DIS/seminars/2013071114001.html.
11. I. T. Habibullin, M. V. Yangubaeva, “Formal diagonalization of a discrete lax operator and conservation laws and symmetries of dynamical systems”, Theoretical and Mathematical Physics, 177(3) (2013), 1655–1679.
12. R. N. Garifullin, A. V. Mikhailov, R. I. Yamilov, “Discrete equation on a square lattice with a nonstandard structure of generalized symmetries”, Theoretical and Mathematical Physics, 180(1) (2014), 765–780.
13. V. E. Zakharov, A. B. Shabat, “Exact theory of two-dimensional self-focusing and onedimensional self-modulation of waves in nonlinear media”, Z.ˇEksper. Teoret. Fiz., 61(1) (1971), 118–134.
14. A. V. Mikhailov, A. B. Shabat, V. V. Sokolov, “The symmetry approach to classification of integrable equations”, Springer Ser. Nonlinear Dynamics, Springer, Berlin, 1991, 115–184.
15. A. V. Mikhailov, editor, “Integrability”, Lecture Notes in Physics, 767 (2009).
16. V. E. Adler, Classification of discrete integrable equations, DSci Thesis, L. D. Landau Institute, 2010.
17. I. Merola, O. Ragnisco, Gui-Zhang Tu, “A novel hierarchy of integrable lattices”, Inverse Problems, 10(6) (1994), 1315–1334.
18. L. A. Takhtadzhyan, V. E. Zakharov, “Equivalence of the nonlinear Schr¨odinger equation and the equation of a Heisenberg ferromagnet”, Theoretical and Mathematical Physics, 38(1) (1979), 26–35.
19. V. E. Zakharov, A. V. Mikhailov, “Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method”, Zh. Eksper. Teoret. Fiz. ` , 74(6) (1978), 1953–1973.
20. A. V. Zhiber, V. V. Sokolov, “Exactly integrable hyperbolic equations of Liouville type”, Uspekhi Mat. Nauk, 56(1(337)) (2001), 63–106.
Дополнительные файлы
Для цитирования: Михайлов А.В. Формальная диагонализация схем Лакса–Дарбу. Моделирование и анализ информационных систем. 2015;22(6):795-817. https://doi.org/10.18255/1818-1015-2015-6-795-817
For citation: Mikhailov A.V. Formal Diagonalisation of Lax-Darboux Schemes. Modeling and Analysis of Information Systems. 2015;22(6):795-817. (In Russ.) https://doi.org/10.18255/1818-1015-2015-6-795-817
Обратные ссылки
- Обратные ссылки не определены.
