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Theses

Méthodes de variétés invariantes pour les équations de Saint Venant et les systèmes hamiltoniens discrets

Abstract : We analyze in this thesis two different problems with invariant manifold methods: the roll-waves phenomenon in hydraulic and the existence of discrete breathers in nonlinear discrete lattices. Roll-waves are periodic and discontinuous travelling waves, entropic solutions of the Saint Venant equations. With the help of Fenichel theorems, we prove the existence of continuous "viscous" roll-waves close to the discontinuous roll-waves when we add a small viscous term in the equations. Then, we study the linear stability of these discontinuous roll-waves. Finally, we prove the existence of small amplitude roll-waves in a channel with a periodic bottom. Discrete breathers are periodic and spatially localized excitations in nonlinear discrete lattices. We first analyze the diatomic Fermi-Pasta-Ulam (FPU) chain. The problem is formulated as a mapping in a loop space. Using a centre manifold reduction, we prove the existence of small amplitude breathers in a diatomic chain with an arbitrary mass ratio. We also use this technique to prove the existence of discrete breathers in ferromagnetic spin chains.
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https://tel.archives-ouvertes.fr/tel-00004405
Contributor : Pascal Noble <>
Submitted on : Friday, January 30, 2004 - 10:23:12 AM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM
Long-term archiving on: : Wednesday, September 12, 2012 - 12:55:56 PM

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  • HAL Id : tel-00004405, version 1

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Pascal Noble. Méthodes de variétés invariantes pour les équations de Saint Venant et les systèmes hamiltoniens discrets. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2003. Français. ⟨tel-00004405⟩

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