Reference |
1. Bak S.M. Existence of periodic travelling waves in systems of nonlinear oscillators on 2D-lattice// Mat.
Stud. – 2011. – V.35, ¹1. – P. 60–65. (in Ukrainian)
2. Áàê Ñ.Ì., Áàðàíîâà Î.Î., Á³ëèê Þ.Ï. Êîðåêòí³ñòü çàäà÷³ Êîø³ äëÿ íåñê³í÷åííî¿ ñèñòåìè íåë³í³éíèõ îñöèëÿòîð³â, ðîçì³ùåíèõ íà äâîâèì³ðí³é ðåø³òö³// Ìàòåìàòè÷íå òà êîìï'þòåðíå ìîäåëþâàííÿ.
Ñåð³ÿ: Ô³çèêî-ìàòåìàòè÷í³ íàóêè: çá. íàóê. ïðàöü. -
Êàì'ÿíåöü-Ïîä³ëüñüêèé: Êàì'ÿíåöü-Ïîä³ëüñüêèé íàö³îíàëüíèé
óí³âåðñèòåò ³ìåí³ ²âàíà Î㳺íêà, 2010. - Âèï. 4. - Ñ. 18-24.
3. Bak S.M., Pankov A.A. The travelling waves in systems of oscillators on 2Dlattice// Ukr. Mat. Visn. –
2010. – V.7, ¹2. – P. 154–175. (in Ukrainian)
4. Âàéíáåðã Ì.Ì., Âàðèàöèîííûé ìåòîä è ìåòîä ìîíîòîííûõ îïåðàòîðîâ. - Ì.: Íàóêà, 1972. - 415 ñ.
5. Êðàñíîñåëüñêèé Ì.À. Òîïîëîãè÷åñêèå ìåòîäû â òåîðèè íåëèíåéíûõ èíòåãðàëüíûõ óðàâíåíèé. - Ì.: Ãîñòåõèçäàò, 1956. - 392 ñ.
6. Reed M., Simon B., Methods of modern mathematical physics. Academic press, New York–San Fransisco,
London, 1975.
7. Aubry S. Breathers in nonlinear lattices: Existence, linear stability and quantization// Physica D. – 1997.
– V.103. – P. 201–250.
8. Bak S.M. Peridoc traveling waves in chains of oscillators// Communications in Mathematical Analysis.
– 2007. – V.3, ¹1. – P. 19–26.
9. Berestycki H., Capuzzo-Dolcetta I., Nirenberg L. Variational methods for indefinite superlinear
homogeneous elliptic problems// Nonlin. Diff. Equat. Appl. – 1995. – V.2. – P. 553-572.
10. Braun O.M., Kivshar Y.S. Nonlinear dynamics of the Frenkel–Kontorova model// Physics Repts. – 1998.
– V.306. – P. 1–108.
11. Braun O.M., Kivshar Y.S., The Frenkel–Kontorova model. – Berlin: Springer, 2004. – 427 p.
12. Butt I., Wattis J. Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice// J. Phys. A: Math.
Gen. – 2006. – V.39. – P. 4955–4984.
13. Feckan M., Rothos V. Traveling waves in Hamiltonian systems on 2D lattices with nearest neighbour
interactions// Nonlinearity. – 2007. – V.20. – P. 319–341.
14. Friesecke G., Matthies K. Geometric solitary waves in a 2D math-spring lattice// Discrete and continuous
dynamical systems. – 2003. – V.3, ¹1. – P. 105–114.
15. Pankov A., Traveling Waves and Periodic Oscillations in Fermi–Pasta–Ulam Lattices. – London – Singapore:
Imperial College Press, 2005. – 196 p.
16. Rabinowitz P., Minimax methods in critical point theory with applications to differential equations. –
Providence, R. I.: American Math. Soc. – 1986. – 100 p.
17. Srikanth P. On periodic motions of two-dimentional lattices// Functional analysis with current applications
in science, technology and industry. – 1998. – V.377. – P. 118–122.
18. Tang C., Guo B. Multiple periodic solutions for two-dimensional lattice dynamic systems// Nonlin.
Analysis. – 2006. – V.65. – P. 1306–1317.
19. Willem M., Minimax theorems. – Boston, Birkh.auser, 1996. – 162 p.
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