ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Bezuglova G. S., Goncharov P. P., Gurov J. V., Chechin G. M. Discrete breathers in scalar dynamical models on the plane square lattice. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 3, pp. 89-103. DOI: 10.18500/0869-6632-2011-19-3-89-103

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Russian
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Journal in the journal
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Article
UDC: 
530.182
DOI: 
10.18500/0869-6632-2011-19-3-89-103

Discrete breathers in scalar dynamical models on the plane square lattice

Autors: 
Bezuglova Galina Sergeevna, Southern Federal University
Goncharov Petr Petrovich, Southern Federal University
Gurov Jurij Vladimirovich, Southern Federal University
Chechin Georgij Mihajlovich, Southern Federal University
Abstract: 

All symmetry related invariant manifolds, admitting localized vibrations, for dynamical models on plane square lattice were found by group­theoretical methods. Discrete breathers were constructed on these manifolds for the model with homogeneous potentials of interparticle interactions and their stability was studied. Nontrivial breather solutions which are not nonlinear normal modes by Rosenberg have been revealed for the above model despite it admits space­time separation of dynamical variables. Discrete breathers of the same type were also found in the system of linear coupled Duffing oscillators situated in sites of square lattice. Our approach for studying discrete breathers can be spread to different two­ and three­dimensional space­periodic dynamical models.

Key words: 
nonlinear dynamics
lattice models
discrete breathers
invariant manifolds
group-theoretical methods
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Received: 
29.12.2010
Accepted: 
14.05.2011
Published: 
29.07.2011
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