Reference |
1. Áàê Ñ.Ì. Áiæó÷i õâèëi â ëàíöþãàõ îñöèëÿòîðiâ// Mat. Stud. – 2006. – Ò.26, ¹2. – Ñ. 140–153.
2. Áàê Ñ.Í., Ïàíêîâ À.À. Áåãóùèå âîëíû â ñèñòåìàõ îñöèëëÿòîðîâ íà äâóìåðíûõ ðåøåòêàõ// Óêðà¿íñüêèé ìàòåìàòè÷íèé âiñíèê. – 2010. – Ò.7, ¹2. – Ñ. 154–175.
3. Âàéíáåðã Ì.Ì. Âàðèàöèîííûé ìåòîä è ìåòîä ìîíîòîííûõ îïåðàòîðîâ. – Ì.: Íàóêà, 1972. – 415 ñ.
4. Êðàñíîñåëüñêèé Ì.À. Òîïîëîãè÷åñêèå ìåòîäû â òåîðèè íåëèíåéíûõ èíòåãðàëüíûõ óðàâíåíèé. –
Ì.: Ãîñòåõèçäàò, 1956. – 392 ñ.
5. Ðèä Ì., Ñàéìîí Á. Ìåòîäû ñîâðåìåííîé ìàòåìàòè÷åñêîé ôèçèêè:  4-õ ò. – Ì.: Ìèð, 1978, Ò.2. –
395 ñ.
6. Aubry S. Breathers in nonlinear lattices: Existence, linear stability and quantization// Physica D. – 1997.
– V.103. – P. 201–250.
7. Bak S.M. Peridoc traveling waves in chains of oscillators// Communications in Mathematical Analysis.
– 2007. – V.3, ¹1. – Ð. 19–26.
8. Braun O.M., Kivshar Y.S. Nonlinear dynamics of the Frenkel–Kontorova model// Physics Repts. – 1998.
– V.306. – P. 1–108.
9. Braun O.M., Kivshar Y.S. The Frenkel–Kontorova model. – Berlin: Springer, 2004. – 427 p.
10. Feckan M., Rothos V. Traveling waves in Hamiltonian systems on 2D lattices with nearest neighbour
interactions// Nonlinearity. – 2007. – V.20. – P. 319–341.
11. 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.
12. Iooss G., Kirchgassner K. Traveling waves in a chain of coupled nonlinear oscillators// Commun. Math.
Phys. – 2000. – V.211. – P. 439–464.
13. Pankov A. Periodic nonlinear Schrodinger equation with an application to photonic crystals// Milan J.
Math. – 2005. – V.73. – P. 259–287.
14. Pankov A. Traveling waves and periodic oscillations in Fermi-Pasta-Ulam lattices. - London–Singapoore:
Imperial College Press, 2005. – 196 p.
15. Rabinowitz P. Minimax methods in critical point theory with applications to differential equations. –
Providence, R. I.: American Math. Soc., 1986. – 100 p.
16. 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.
17. Willem M. Minimax theorems. - Boston, Birkh¨auser, 1996. – 162 p.
|