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

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Ivanchenko M. V. Mode localization in Fermi-Pasta-Ulam chains with arbitrary degree of nonlinearity. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 1, pp. 55-62. DOI: 10.18500/0869-6632-2011-19-1-55-62

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Language: 
Russian
Heading: 
Nonlinear Waves. Solitons
Article type: 
Article
UDC: 
530.182, 534.1, 534.015
DOI: 
10.18500/0869-6632-2011-19-1-55-62

Mode localization in Fermi-Pasta-Ulam chains with arbitrary degree of nonlinearity

Autors: 
Ivanchenko Mihail Vasilevich, Lobachevsky State University of Nizhny Novgorod
Abstract: 

q-Breathers are exact periodic solutions of nonlinear acoustic chain systems, exponentially localized in the space of normal modes. Their presence determines the energy localization in initially excited modes, the absence of thermalization and persistence of quasi-linear spectrum. In the present paper we study the influence of the order of nonlinearity γ on the localization length in the q-space, delocalization threshold and scaling of these properties with the system size. It is shown that the exponential localization holds; moreover, there exists the critical value γ = 6, above which the localization strengthens with increasing the chain length. Accordingly, in case of mixed order nonlinearities thermalization/strong chaos thresholds in large systems are determined by nonlinear terms with γ ≤ 6 only. 

Key words: 
Nonlinear modes
energy localization
q-breathers
Reference: 
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Received: 
15.07.2010
Accepted: 
21.01.2011
Published: 
29.04.2011
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