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Equations describing the evolution of particles, solitons, or localized structures, driven by a zero-average, periodic, external force, and invariant under time reversal and a half-period time shift, exhibit a ratchet current when the driving force breaks these symmetries. The bi-harmonic force $f(t)=epsilon_1cos(q omega t+phi_1)+epsilon_2cos(pomega t+phi_2)$ does it for almost any choice of $phi_{1}$ and $phi_{2}$, provided $p$ and $q$ are two co-prime integers such that $p+q$ is odd. It has been widely observed, in experiments in Josephson-junctions, photonic crystals, etc., as well as in simulations, that the ratchet current induced by this force has the shape $vproptoepsilon_1^pepsilon_2^qcos(p phi_{1} - q phi_{2} + theta_0)$ for small amplitudes, where $theta_0$ depends on the damping ($theta_0=pi/2$ if there is no damping, and $theta_0=0$ for overdamped systems). We rigorously prove that this precise shape can be obtained solely from the broken symmetries of the system and is independent of the details of the equation describing the system.
Ratchets are devices able to rectify an otherwise oscillatory behavior by exploiting an asymmetry of the system. In rocking ratchets the asymmetry is induced through a proper choice of external forces and modulations of nonlinear symmetric potentials
The operation of Brownian motors is usually described in terms of out-of-equilibrium and symmetry-breaking settings, with the relevant spatiotemporal symmetries identified from the analysis of the equations of motion for the system at hand. When the
The generation of high-intensity optical fields from harmonic-wave photons, interacting via a cross-phase modulation with dark solitons both propagating in a Kerr nonlinear medium, is examined. The focus is on a pump consisting of time-entangled dark
We report on the experimental study of an optically driven multimode semiconductor laser with 1~m cavity length. We observed a spatiotemporal regime where real time measurements reveal very high intensity peaks in the laser field. Such a regime, whic
We numerically study the breathing dynamics induced by collision between bright solitons in the one-dimensional Bose-Einstein condensates with strong dipole-dipole interaction. This breathing phenomenon is closely related to the after-collision short