Search results for "soliton"
showing 10 items of 534 documents
A SUBCRITICAL BIFURCATION FOR A NONLINEAR REACTION–DIFFUSION SYSTEM
2010
In this paper the mechanism of pattern formation for a reaction-diffusion system with nonlinear diffusion terms is investigated. Through a linear stability analysis we show that the cross-diffusion term allows the pattern formation. To predict the form and the amplitude of the pattern we perform a weakly nonlinear analysis. In the supercritical case the Stuart-Landau equation is found, which rules the evolution of the amplitude of the most unstable mode. With the increasing distance from the bifurcation value of the cross-diffusion parameter, the weakly nonlinear analysis fails and a Fourier–Galerkin approach is adopted. In the subcritical case the weakly nonlinear analysis must be pushed u…
Breather dynamics in a stochastic sine-Gordon equation: evidence of noise-enhanced stability
2023
The dynamics of sine-Gordon breathers is studied in the presence of dissipative and stochastic perturbations. Taking a stationary breather with a random phase value as the initial state, the performed simulations demonstrate that a spatially-homogeneous noisy source can make the oscillatory excitation more stable, i.e., it enables the latter to last significantly longer than it would in a noise-free scenario. Both the frequency domain and the localization of energy are examined to document the effectiveness of the noise-enhanced stability phenomenon, which emerges as a nonmonotonic behavior of an average characteristic time for the breather as a function of the noise intensity. The influenc…
Supplementary optical phase transition in photorefractive coherent oscillator
2001
The semilinear photorefractive coherent oscillator with two counterpropagating pump waves may exhibit two optical phase transitions: one from a disordered state of wide-angle photorefractive scattering into a high-ordered state with the immobile photorefractive grating and the other one from the state with immobile grating into the state with two moving photorefractive gratings. We show, both experimentally and from calculations, that two these phase transitions are the second-order phase transitions.
Stability of laser cavity-solitons for metrological applications
2023
Laser cavity-solitons can appear in systems comprised of a nonlinear microcavity nested within an amplifying fiber loop. These states are robust and self-emergent and constitute an attractive class of solitons that are highly suitable for microcomb generation. Here, we present a detailed study of the free-running stability properties of the carrier frequency and repetition rate of single solitons, which are the most suitable states for developing robust ultrafast and high repetition rate comb sources. We achieve free-running fractional stability on both optical carrier and repetition rate (i.e., 48.9 GHz) frequencies on the order of [Formula: see text] for a 1 s gate time. The repetition r…
Anharmonic effects on the dynamic behavior’s of Klein Gordon model’s
2021
Abstract This work completes and extends the Ref. Tchakoutio Nguetcho et al. (2017), in which we have focused our attention only on the dynamic behavior of gap soliton solutions of the anharmonic Klein-Gordon model immersed in a parameterized on-site substrate potential. We expand our work now inside the permissible frequency band. These considerations have crucial effects on the response of nonlinear excitations that can propagate along this model. Moreover, working in the allowed frequency band is not only interesting from a physical point of view, it also provides an extraordinary mathematical model, a new class of differential equations possessing vital parameters and vertical singular …
Modulational instability in resonant optical fiber with higher-order dispersion effect
2010
International audience; The modulational instability (MI) of an electromagnetic wave in a resonant optical fiber with a two-level system is investigated. In the normal dispersion regime, we find the occurrence of nonconventional MI sidebands which are induced by the two-level resonant atoms. We also observe that the MI gain spectra are suppressed by the higher-order dispersion effect in the anomalous dispersion regime.
Temporal Soliton “Molecules” in Mode-Locked Lasers: Collisions, Pulsations, and Vibrations
2008
A few years after the discovery of the stable dissipative soliton pairs in passively mode-locked lasers, a large variety of multi-soliton complexes were studied in both experiments and numerical simulations, revealing interesting new behaviors. This chapter focuses on the following three subjects: collisions between dissipative solitons, pulsations of dissipative solitons, and vibrations of soliton pairs. Different outcomes of collisions between a soliton pair and a soliton singlet are discussed, showing possible experimental control in the formation or dissociation of ‘soliton molecules’. Long-period pulsations of single and multiple dissipative solitons are presented as limit cycles and o…
Spectral incoherent solitons
2009
Solitons have been usually considered as inherently coherent localized structures and the discovery of incoherent optical solitons has represented a significant progress [1]. As occurs for standard coherent solitons, incoherent solitons are characterized by a confinement of the field in the spatial or in the temporal domain. We introduce here a novel type of incoherent solitons that are neither spatial nor temporal, i.e., the incoherent field does not exhibit any confinement in the spatiotemporal domain; however, the uncorrelated frequency components that constitute the incoherent field exhibit a localized soliton behavior in the frequency domain [2].
Coherent vector pi-pulse in optical amplifiers
2007
We obtain an exact vector solitary solution for the amplification of an optical pulse with a time width short compared with both population and polarization decay time. This dissipative soliton results from the balance between the gain from inverted resonant two-level atoms and the linear loss of the host material. We suppose that the excited state of the active centers is degenerate on the projection of the angular moment. Numerical simulations demonstrate the stability of these vector dissipative solitons in the presence of both linear birefringence and group velocity dispersion of the host material.
Comb-like Turing patterns embedded in Hopf oscillations: Spatially localized states outside the 2:1 frequency locked region
2017
A generic distinct mechanism for the emergence of spatially localized states embedded in an oscillatory background is demonstrated by using 2:1 frequency locking oscillatory system. The localization is of Turing type and appears in two space dimensions as a comb-like state in either $\pi$ phase shifted Hopf oscillations or inside a spiral core. Specifically, the localized states appear in absence of the well known flip-flop dynamics (associated with collapsed homoclinic snaking) that is known to arise in the vicinity of Hopf-Turing bifurcation in one space dimension. Derivation and analysis of three Hopf-Turing amplitude equations in two space dimensions reveals a local dynamics pinning mec…