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Non-equilibrium dissipative systems usually exhibit multistability, leading to the presence of propagative domain between steady states. We investigate the front propagation into an unstable state in discrete media. Based on a paradigmatic model of coupled chain of oscillators and populations dynamics, we calculate analytically the average speed of these fronts and characterize numerically the oscillatory front propagation. We reveal that different parts of the front oscillate with the same frequency but with different amplitude. To describe this latter phenomenon we generalize the notion of the Peierls-Nabarro potential, achieving an effective continuous description of the discreteness effect.
This paper is an introductory review of the problem of front propagation into unstable states. Our presentation is centered around the concept of the asymptotic linear spreading velocity v*, the asymptotic rate with which initially localized perturba
We discuss the front propagation in ferroelectric chiral smectics (SmC*) subjected to electric and magnetic fields applied parallel to smectic layers. The reversal of the electric field induces the motion of domain walls or fronts that propagate into
Evidence is presented of universal behavior in modulationally unstable media. An ensemble of nonlinear evolution equations, including three partial differential equations, an integro-differential equation, a nonlocal system and a differential-differe
We study evolution of pulses propagating through focusing nonlinear media. Small disturbance on the smooth initial non-uniform background leads to formation of the region of strong nonlinear oscillations. We develop here an asymptotic method for find
Front propagation in two dimensional steady and unsteady cellular flows is investigated in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. In the steady case, by means of a simplified model, we provide an analy