Pinning-depinning transition of fronts between standing waves

Abstract : Dynamic behaviors of fronts connecting standing waves, such as the locking phenomenon, pinning-depinning transitions, propagation, and front interactions, are studied. Two systems are considered, a vertically driven pendulum chain and a generalized ϕ4 model. Both models exhibit in an appropriate region of parameters bistability between standing waves. In the driven pendulum chain, using a Galerkin expansion we characterize the region of bistability between subharmonic waves for the upright and the upside-down pendulum states. We derive analytically the front dynamics in the generalized ϕ4 model, showing regions where fronts are oscillatory or propagative. We also characterize the mechanism of the pinning-depinning transition of fronts between standing waves. Using front interactions we predict the emergence of dissipative localized waves supported on a standing wave and characterize their corresponding homoclinic snaking bifurcation diagrams. All these analytical predictions are confirmed by numerical simulations with quite good agreement.
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Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2013, 87, pp.12901. 〈10.1103/PHYSREVE.87.012901〉
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https://hal.archives-ouvertes.fr/hal-00944230
Contributeur : Saliya Coulibaly <>
Soumis le : lundi 10 février 2014 - 13:37:28
Dernière modification le : mardi 3 juillet 2018 - 11:33:28

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Marcel G. Clerc, Cristian Fernández-Oto, Saliya Coulibaly. Pinning-depinning transition of fronts between standing waves. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2013, 87, pp.12901. 〈10.1103/PHYSREVE.87.012901〉. 〈hal-00944230〉

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