DISCRETE BREATHERS IN SCALAR DYNAMICAL MODELS ON THE PLANE SQUARE LATTICE
Cite this article as:
Bezuglova . S., Goncharov P. P., Gurov Y. V., Chechin G. М. 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: https://doi.org/10.18500/0869-6632-2011-19-3-89-103
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.
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BibTeX
author = { G. S. Bezuglova and P. P. Goncharov and Yu. V. Gurov and G М. Chechin},
title = {DISCRETE BREATHERS IN SCALAR DYNAMICAL MODELS ON THE PLANE SQUARE LATTICE},
year = {2011},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {19},number = {3},
url = {https://old-andjournal.sgu.ru/en/articles/discrete-breathers-in-scalar-dynamical-models-on-the-plane-square-lattice},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2011-19-3-89-103},pages = {89--103},issn = {0869-6632},
keywords = {nonlinear dynamics,lattice models,discrete breathers,invariant manifolds,grouptheoretical methods.},
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. }}