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

For citation:

Landa P. S., Ushakov V. G., Ebeling W. Self-oscillations in dissipative ring Toda chain. Izvestiya VUZ. Applied Nonlinear Dynamics, 2000, vol. 8, iss. 6, pp. 44-52. DOI: 10.18500/0869-6632-2000-8-6-44-52

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Language: 
Russian
Heading: 
Autowaves. Self-organization
Article type: 
Article
UDC: 
534.1
DOI: 
10.18500/0869-6632-2000-8-6-44-52

Self-oscillations in dissipative ring Toda chain

Autors: 
Landa Polina Solomonovna, Lomonosov Moscow State University
Ushakov Vadim Gennadevich, Lomonosov Moscow State University
Ebeling Werner, Humboldt University of Berlin
Abstract: 

We study here different modes of self-oscillations in ring Toda chain with negative friction. Assuming that at small friction the shape of self-oscillations is close to one of the known Toda soliton-like solutions we use analytical methods in combination with numerical ones for study о the self-oscillations. We show that а Toda chain consisting of N elements possesses N+1 different modes of self-oscillations. Among them two modes correspond to left and right rotations of the chain as a whole with a constant velocity. Each of the other modes represents а combination of moving soliton and the rotation with a velocity depending on the mode number. Only for the mode corresponding to anti-phase oscillation of the chain neighboring elements (such oscillation are possible for an even N) the constant component of velocity is equal to zero.

Key words: 
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Received: 
23.09.2000
Accepted: 
19.01.2001
Published: 
25.03.2001
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