Related papers: Parametric localized patterns and breathers in dis…
Previous studies of lasers and nonlinear resonators have revealed that the polarisation degree of freedom allows for the formation of polarisation patterns and novel localized structures, such as vectorial defects. Type II optical…
We explore the dynamics of strongly localized periodic solutions (discrete solitons, or discrete breathers) in a finite one-dimensional chain of asymmetric vibro-impact oscillators. The model involves a parabolic on-site potential with…
We examine the dynamics of strongly localized periodic solutions (discrete breathers) in two-dimensional array of coupled finite one-dimensional chains of oscillators. Localization patterns with both single and multiple localization sites…
We report on the experimental generation of discrete breather states (intrinsic localized modes) in frustrated Josephson arrays. Our experiments indicate the formation of discrete breathers during the transition from the static to the…
Numerical studies together with asymptotic and spectral analysis establish regimes where soliton pairs in degenerate optical parametric oscillators fuse, repel, or form bound states. A novel bound state stabilized by coupled internal…
Localized patterns in singularly perturbed reaction-diffusion equations typically consist of slow parts -- in which the associated solution follows an orbit on a slow manifold in a reduced spatial dynamical system -- alternated by fast…
Localised structures appear in a wide variety of systems, arising from a pinning mechanism due to the presence of a small-scale pattern or an imposed grid. When there is a separation of lengthscales, the width of the pinning region is…
In pattern-forming systems, localized patterns are readily found when stable patterns exist at the same parameter values as the stable unpatterned state. Oscillons are spatially localized, time-periodic structures, which have been found…
From cytoskeletal networks to tissues, many biological systems behave as active materials. Their composition and stress-generation is affected by chemical reaction networks. In such systems, the coupling between mechanics and chemistry…
A model for a monolayer of two types of particles spontaneously forming ordered patterns is studied by a mesoscopic theory and by MC simulations. We assume hard-cores of the same size for both components, short-range attraction long-range…
The regions of existence and stability of dark solitons in the Lugiato-Lefever model with normal chromatic dispersion are described. These localized states are shown to be organized in a bifurcation structure known as collapsed snaking…
We study localised activity patterns in neural field equations posed on the Euclidean plane; such models are commonly used to describe the coarse-grained activity of large ensembles of cortical neurons in a spatially continuous way. We…
We propose a phenomenological model for pattern formation in a vertically vibrated layer of granular material. This model exhibits a variety of stable cellular patterns including standing rolls and squares as well as localized objects…
We consider an array of nearest-neighbor coupled nonlinear autonomous oscillators with quenched random frequencies and purely conservative coupling. We show that global phase-locked states emerge in finite lattices and study numerically…
The position and motion of localized states of light in propagative geometries can be controlled via an adequate parameter modulation. Here, we show theoretically and experimentally that this process can be accurately described as the phase…
The Kuramoto model is a commonly used mathematical model for studying synchronized oscillations in biological systems, with its temporal synchronization properties well studied. However, the properties of spatial waves have received less…
A new strategy for trapping quantum particles is presented, which behaves like an effective harmonic oscillator potential trap wherever is desired. The approach is based on harmonic contraction and expansion of the system around a fixed…
We present analytical and numerical studies of phase-coherent dynamics of intrinsically localized excitations (breathers) in a system of two weakly coupled nonlinear oscillator chains. We show that there are two qualitatively different…
The origin, stability and bifurcation structure of different types of bright localized structures described by the Lugiato-Lefever equation is studied. This mean field model describes the nonlinear dynamics of light circulating in fiber…
Chimera states for the one-dimensional array of nonlocally coupled phase oscillators in the continuum limit are assumed to be stationary states in most studies, but a few studies report the existence of breathing chimera states. We focus on…