title: 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 φ(4) 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 φ(4) 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.
authors: Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago Chile. marcel@dfi.uchile.cl
authors: Marcel G
authors: MG
authors: Clerc
authors: Cristian
authors: C
authors: Fernández-Oto
authors: Saliya
authors: S
authors: Coulibaly
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D012212:Rheology / Q000379:methods*