DISCRETE BREATHERS AND QUASIBREATHERS IN NONLINEAR MONOATOMIC CHAINS
Cite this article as:
Goncharov P. P., Dzhelauhova G. S., Chechin G. М. DISCRETE BREATHERS AND QUASIBREATHERS IN NONLINEAR MONOATOMIC CHAINS. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 6, pp. 57-74. DOI: https://doi.org/10.18500/0869-6632-2007-15-6-57-74
We study the stability of the symmetric and antisymmetric discrete breathers in the monoatomic chain described by potential energy which is a uniform function of the fourth order. It is shown that the change of the stability properties of these two dynamical objects (known as Sievers-Takeno and Page modes, respectively) takes place at the same strength of the inter-site interactions with respect to the on-site interactions. We also present a new method (the «pair synchronization» method) for the discrete breather construction in the arbitrary nonlinear Hamiltonian lattices. This method possesses an explicit physical sense. Its application technique is demonstrated with the chain of linear coupled Duffing oscillators. The concept of quasibreathers which represent the dynamical objects corresponded to small deviations from the exact breather solutions is briefly discussed.
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BibTeX
author = {P. P. Goncharov and G. S. Dzhelauhova and G М. Chechin},
title = {DISCRETE BREATHERS AND QUASIBREATHERS IN NONLINEAR MONOATOMIC CHAINS},
year = {2007},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {15},number = {6},
url = {https://old-andjournal.sgu.ru/en/articles/discrete-breathers-and-quasibreathers-in-nonlinear-monoatomic-chains},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2007-15-6-57-74},pages = {57--74},issn = {0869-6632},
keywords = {-},
abstract = {We study the stability of the symmetric and antisymmetric discrete breathers in the monoatomic chain described by potential energy which is a uniform function of the fourth order. It is shown that the change of the stability properties of these two dynamical objects (known as Sievers-Takeno and Page modes, respectively) takes place at the same strength of the inter-site interactions with respect to the on-site interactions. We also present a new method (the «pair synchronization» method) for the discrete breather construction in the arbitrary nonlinear Hamiltonian lattices. This method possesses an explicit physical sense. Its application technique is demonstrated with the chain of linear coupled Duffing oscillators. The concept of quasibreathers which represent the dynamical objects corresponded to small deviations from the exact breather solutions is briefly discussed. }}