Reference |
1. Бак С.М. Бiжучi хвилi в ланцюгах осциляторiв// Mat. Stud. – 2006. – Т.26, №2. – С. 140–153.
2. Бак С.Н., Панков А.А. Бегущие волны в системах осцилляторов на двумерных решетках// Український математичний вiсник. – 2010. – Т.7, №2. – С. 154–175.
3. Вайнберг М.М. Вариационный метод и метод монотонных операторов. – М.: Наука, 1972. – 415 с.
4. Красносельский М.А. Топологические методы в теории нелинейных интегральных уравнений. –
М.: Гостехиздат, 1956. – 392 с.
5. Рид М., Саймон Б. Методы современной математической физики: В 4-х т. – М.: Мир, 1978, Т.2. –
395 с.
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, №1. – Р. 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, №1. – 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, BirkhЁauser, 1996. – 162 p.
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