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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_2005_196_2_a2,
     author = {Yu. S. Kolesov and A. E. Khar'kov},
     title = {Similarity and difference in the dynamics of plane and 3-dimensional non-linear waves},
     journal = {Sbornik. Mathematics},
     pages = {201--229},
     publisher = {mathdoc},
     volume = {196},
     number = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_2_a2/}
}
TY  - JOUR
AU  - Yu. S. Kolesov
AU  - A. E. Khar'kov
TI  - Similarity and difference in the dynamics of plane and 3-dimensional non-linear waves
JO  - Sbornik. Mathematics
PY  - 2005
SP  - 201
EP  - 229
VL  - 196
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2005_196_2_a2/
LA  - en
ID  - SM_2005_196_2_a2
ER  - 
%0 Journal Article
%A Yu. S. Kolesov
%A A. E. Khar'kov
%T Similarity and difference in the dynamics of plane and 3-dimensional non-linear waves
%J Sbornik. Mathematics
%D 2005
%P 201-229
%V 196
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2005_196_2_a2/
%G en
%F SM_2005_196_2_a2
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/