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This article is cited in 1 scientific paper (total in 1 paper)
Asymptotic analysis of the parametric instability of nonlinear hyperbolic equations
V. S. Belonosovab a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Abstract:
This paper is concerned with parametric resonance under nonlinear periodic perturbations of differential equations which are abstract analogues of hyperbolic systems. A modification of the Krylov-Bogolyubov averaging method capable of circumventing the well-known small divisor problem is applied to reduce the description of solutions of perturbed equations at resonance to the study of autonomous dynamical systems in finite-dimensional spaces.
Bibliography: 28 titles.
Keywords:
hyperbolic equations, parametric resonance, averaging method.
Received: 14.12.2016 and 03.04.2017
Citation:
V. S. Belonosov, “Asymptotic analysis of the parametric instability of nonlinear hyperbolic equations”, Sb. Math., 208:8 (2017), 1088–1112
Linking options:
https://www.mathnet.ru/eng/sm8883https://doi.org/10.1070/SM8883 https://www.mathnet.ru/eng/sm/v208/i8/p4
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