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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 4, Pages 628–645 (Mi zvmmf6)  
Features of the dynamics of nonlinear waves in plane domains

Yu. S. Kolesov, A. E. Khar'kov

Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia
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Abstract: An analysis of the dynamics of three-dimensional nonlinear waves on a torus has shown that their attractors are the so-called self-organization regimes, which are created from trajectories crowding together and have several remarkable features. Specifically, they are well ordered with respect to spatial and time variables, and their energy is fairly high and decreases gradually with decreasing elasticity coefficient, which itself evolves into a diffusion chaos. The role of this paper is twofold. First, the features of self-organization regimes are analyzed in the case of Neumann boundary conditions. Second, the stages leading to the detection of this phenomenon are described in detail.
Key words: multiplicity of the spectrum of the Laplacian, quasi-normal form, Galerkin method, self-organization regimes and their energy.
Received: 16.05.2008
English version:
Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 4, Pages 606–622
DOI: https://doi.org/10.1134/S096554250904006X
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: Yu. S. Kolesov, A. E. Khar'kov, “Features of the dynamics of nonlinear waves in plane domains”, Zh. Vychisl. Mat. Mat. Fiz., 49:4 (2009), 628–645; Comput. Math. Math. Phys., 49:4 (2009), 606–622
Citation in format AMSBIB
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