Geodesic
On the dynamics of the piecewise-linear model of the Swift--Hohenberg equation
Russian journal of nonlinear dynamics, Tome 5 (2009) no. 4, pp. 569-583.

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

In this paper we study the piecewise-linear model of the stationary Swift–Hohenberg equation well known in mathematical physics, which provides explicit front type solutions. Due to the reversibility relative to two involutions of the corresponding Hamiltonian system, this involves the existence of a heteroclinic contour connecting two saddle-foci. Using methods of symbolic dynamics, we give a description of all solutions lying in the neighborhood of the contour at the level of the Hamiltonian containing the contour.
Keywords: Swift–Hohenberg equation, Hamiltonian system, saddle focus, symbolic dynamics.
Mots-clés : fronts, heteroclinic contour 
@article{ND_2009_5_4_a8,
     author = {L. M. Lerman and N. A. Slinyakova},
     title = {On the dynamics of the piecewise-linear model of the {Swift--Hohenberg} equation},
     journal = {Russian journal of nonlinear dynamics},
     pages = {569--583},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2009_5_4_a8/}
}
TY  - JOUR
AU  - L. M. Lerman
AU  - N. A. Slinyakova
TI  - On the dynamics of the piecewise-linear model of the Swift--Hohenberg equation
JO  - Russian journal of nonlinear dynamics
PY  - 2009
SP  - 569
EP  - 583
VL  - 5
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2009_5_4_a8/
LA  - ru
ID  - ND_2009_5_4_a8
ER  - 
%0 Journal Article
%A L. M. Lerman
%A N. A. Slinyakova
%T On the dynamics of the piecewise-linear model of the Swift--Hohenberg equation
%J Russian journal of nonlinear dynamics
%D 2009
%P 569-583
%V 5
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2009_5_4_a8/
%G ru
%F ND_2009_5_4_a8
L. M. Lerman; N. A. Slinyakova. On the dynamics of the piecewise-linear model of the Swift--Hohenberg equation. Russian journal of nonlinear dynamics, Tome 5 (2009) no. 4, pp. 569-583. http://geodesic.mathdoc.fr/item/ND_2009_5_4_a8/