Search results for "Pattern formation"
showing 10 items of 408 documents
Ultrasonic cavity solitons
2007
We report on a new type of localized structure, an ultrasonic cavity soliton, supported by large aspect-ratio acoustic resonators containing viscous media. These states of the acoustic and thermal fields are robust structures, existing whenever a spatially uniform solution and a periodic pattern coexist. Direct proof of their existence is given both through the numerical integration of the model and through the analysis and numerical integration of a generalized Swift-Hohenberg equation, derived from the microscopic equations under conditions close to nascent bistability. An analytical solution for the ultrasonic cavity soliton is given.
Phase-bistable Kerr cavity solitons and patterns
2013
We study pattern formation in a passive nonlinear optical cavity on the basis of the classic Lugiato-Lefever model with a periodically modulated injection. When the injection amplitude sign alternates, e.g., following a sinusoidal modulation in time or in space, a phase-bistable response emerges, which is at the root of the spatial pattern formation in the system. An asymptotic description is given in terms of a damped nonlinear Schr\"odinger equation with parametric amplification, which allows gaining insight into the basic spatiotemporal dynamics of the system. One- and two-dimensional phase-bistable spatial patterns, such as bright and dark-ring cavity solitons and labyrinths, are demons…
Hydrodynamics of periodic breathers
2014
We report the first experimental observation of periodic breathers in water waves. One of them is Kuznetsov–Ma soliton and another one is Akhmediev breather. Each of them is a localized solution of the nonlinear Schrödinger equation (NLS) on a constant background. The difference is in localization which is either in time or in space. The experiments conducted in a water wave flume show results that are in good agreement with the NLS theory. Basic features of the breathers that include the maximal amplitudes and spectra are consistent with the theoretical predictions.
Tenth Peregrine breather solution to the NLS equation
2015
We go on in this paper, in the study of the solutions of the focusing NLS equation. With a new representation given in a preceding paper, a very compact formulation without limit as a quotient of two determinants, we construct the Peregrine breather of order N=10. The explicit analytical expression of the Akhmediev's solution is completely given.
Two-dimensional mobile breather scattering in a hexagonal crystal lattice.
2021
We describe the full two-dimensional scattering of long-lived breathers in a model hexagonal lattice of atoms. The chosen system, representing an idealized model of mica, combines a Lennard-Jones interatomic potential with an “egg-box” harmonic potential well surface. We investigate the dependence of breather properties on the ratio of the well depths associated with the interaction and on-site potentials. High values of this ratio lead to large spatial displacements in adjacent chains of atoms and thus enhance the two-dimensional character of the quasi-one-dimensional breather solutions. This effect is further investigated during breather-breather collisions by following the constrained en…
All-optical discrete vortex switch
2011
We introduce discrete vortex solitons and vortex breathers in circular arrays of nonlinear waveguides. The simplest vortex breather in a four-waveguide coupler is a nonlinear dynamic state changing its topological charge between $+1$ and $\ensuremath{-}1$ periodically during propagation. We find the stability domain for this solution and suggest an all-optical vortex switching scheme.
Collision of Akhmediev Breathers in Nonlinear Fiber Optics
2013
We report here a novel fiber-based test bed using tailored spectral shaping of an optical-frequency comb to excite the formation of two Akhmediev breathers that collide during propagation. We have found specific initial conditions by controlling the phase and velocity differences between breathers that lead, with certainty, to their efficient collision and the appearance of a giant-amplitude wave. Temporal and spectral characteristics of the collision dynamics are in agreement with the corresponding analytical solution. We anticipate that experimental evidence of breather-collision dynamics is of fundamental importance in the understanding of extreme ocean waves and in other disciplines dri…
Topological charge selection rule for phase singularities
2009
We present a study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the underlying symmetry is emphasized. An effective model describing the short range dynamics of the vortex clusters has been designed. A method to engineer any desired configuration of clusters of phase singularities is proposed. Its flexibility to create and control clusters of vortices is discussed.
Universal description of pattern formation in optical oscillators under bichromatic injection
2018
We study pattern formation in a complex Swift–Hohenberg equation with phase-sensitive (parametric) gain. Such an equation serves as a universal order parameter equation describing the onset of spontaneous oscillations in extended systems submitted to a bichromatic injection when the instability is toward long (transverse) wavelengths. Applications include two-level lasers and photorefractive oscillators. Under such an injection, the original continuous phase symmetry of the system is replaced by a discrete one and phase bistability emerges. This leads to the spontaneous formation of phase-locked spatial structures, such as phase domains and dark-ring (phase) cavity solitons. The stability o…
Pattern formation through phase bistability in oscillatory systems with space-modulated forcing.
2010
We propose a novel forcing technique of spatially extended self-oscillatory systems able to excite phase bistability and the dissipative structures associated with it. The forcing is time periodic at a frequency close to the oscillators' frequency and is spatially modulated. The effects of this type of forcing are demonstrated analytically and numerically in a directly driven complex Ginzburg-Landau equation. Both spatially periodic and spatially random drives prove to be effective.