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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2009, Volume 5, Number 4, Pages 569–583
(Mi nd113)
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This article is cited in 1 scientific paper (total in 1 paper)
On the dynamics of the piecewise-linear model of the Swift–Hohenberg equation
L. M. Lermanab, N. A. Slinyakovab a Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod
b N. I. Lobachevski State University of Nizhni Novgorod, Faculty of Mechanics and Mathematics
Abstract:
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, fronts, heteroclinic contour, Hamiltonian system, saddle focus, symbolic dynamics.
Received: 06.10.2009
Citation:
L. M. Lerman, N. A. Slinyakova, “On the dynamics of the piecewise-linear model of the Swift–Hohenberg equation”, Nelin. Dinam., 5:4 (2009), 569–583
Linking options:
https://www.mathnet.ru/eng/nd113 https://www.mathnet.ru/eng/nd/v5/i4/p569
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Abstract page: | 203 | Full-text PDF : | 79 | First page: | 1 |
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