Geodesic
Similarity and difference in the dynamics of plane and 3-dimensional non-linear waves
Sbornik. Mathematics, Tome 196 (2005) no. 2, pp. 201-229 Cet article a éte moissonné depuis la source Math-Net.Ru

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The method of quasinormal forms is used to demonstrate the mild loss of stability by travelling waves on a circle and a torus. The dynamics in the case of a small elastic-constraint coefficient is studied in a model example. The results obtained and an explicit difference scheme developed expressly for the problem are used in a series of numerical experiments. As a result one distinguishes a subdomain of the parameter space in which the most important features of the dynamics on a torus and a circle are related to self-organisation regimes, where self-organisation regimes on a circle are versions of certain similar regimes on a torus. 
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Yu. S. Kolesov; A. E. Khar'kov. Similarity and difference in the dynamics of plane and 3-dimensional non-linear waves. Sbornik. Mathematics, Tome 196 (2005) no. 2, pp. 201-229. http://geodesic.mathdoc.fr/item/SM_2005_196_2_a2/

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