Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1607.02113

Pattern formation in a complex Swift-Hohenberg equation with phase bistability

Manuel Martínez-Quesada·Germán J. de Valcárcel
View original source ↗Read source document ↗Export metadata ↓

Abstract

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 kind of forcing dubbed rocking when the instability is towards long wavelengths. Applications include two-level lasers and photorefractive oscillators. Under rocking, the original continuous phase symmetry of the system is replaced by a discrete one, so that phase bistability emerges. This leads to the spontaneous formation of phase-locked spatial structures like phase domains and dark-ring (phase-) cavity solitons. Stability of the homogeneous solutions is studied and numerical simulations are made covering all the dynamical regimes of the model, which turn out to be very rich. Formal derivations of the rocked complex Swift-Hohenberg equation, using multiple scale techniques, are given for the two-level laser and the photorefractive oscillator.

Explore related subjects

nlin.PSphysics.optics

Keep this discovery

BibTeXRIS

Manuel Martínez-Quesada, Germán J. de Valcárcel. 2016-07-07. Pattern formation in a complex Swift-Hohenberg equation with phase bistability. https://arxiv.org/abs/1607.02113

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Self-similar vector solitons for the coupled higher-order nonlinear Schrodinger equations in inhomogeneous optical fibers

We prove the existence of two kinds of self-similar vector solitons in an inhomogeneous optical fiber medium, where light propagation is governed by a pair of coupled higher-order nonlinear Schrodinger equations with varying second- and third-order dispersions, self- and cross-phase modulation non linearities, self-steepening, and linear gain/loss effects. The newly found self-similar waves comprise bright-W-shaped and kink-antikink waveforms with nonvanishing amplitudes. As a practical exam ple, we discuss the propagation dynamics of these soliton structures in a periodically distributed fiber system as well as an exponential dispersion-decreasing fiber. The results demonstrate that the parameter functions of gain/loss and third-order dispersion serve as a key factor in determining the nonlinear dynamics of self-similar vector solitons. In particular, we find that precise control over the shape and dynamic evolution of self-similar pulses can be achieved through a proper choice of the distributed third-order dispersion parameter, while the gain/loss coefficient controls their intensity.

nlin.PS↗
arXiv2026

Fast Synergetic Simulation to Study Slow Evolution of Soliton Patterns in Optical Resonators

Complex patterns in physical and biological systems often emerge through slow collective dynamics governed by a small number of key variables. In nonlinear optical resonators, dissipative Kerr solitons provide an important example, where interactions between well-separated solitons can evolve over timescales far longer than the characteristic loss and gain timescales. Direct numerical simulation of these dynamics is challenging because stiffness forces conventional methods to resolve many rapidly damped degrees-of-freedom with very small time steps. We present a numerical scheme, the synergetic method, that eliminates these rapidly damped degrees-of-freedom and retains the slowly evolving modes, enabling time steps many orders of magnitude larger than those used in conventional approaches. Applied to soliton molecules in driven Kerr cavities, the method achieves speedups of $10^3$ to $10^5$ while capturing dynamics on laboratory timescales. We use it to model the full interaction dynamics of a three-soliton molecule and the evolution of an eight-soliton molecule. The approach provides an efficient framework for studying slow pattern formation in nonlinear systems with widely separated timescales.

nlin.PS↗
arXiv2026

Breathers in solitonic room-temperature superlattice-induced superfluorescence in quasi-2D perovskites

Recently, a soliton mechanism for room-temperature superfluorescence in thin perovskite films has been proposed, with a fundamental soliton predicted to remain stable under LO phonon--exciton interactions. At the same time, superlattice architectures offer a route to enhancing superfluorescence in perovskites. Motivated by recent observations of room-temperature superfluorescence in periodic superlattices of quasi-2D metal-halide perovskites, we extend the 2D nonlocal nonlinear Schr\"odinger equation describing Wannier exciton--LO phonon interactions to superlattice structures, obtaining a 3D nonlocal nonlinear Schr\"odinger equation. We show that interlayer tunnelling gives rise to breather dynamics corresponding to a stable fundamental soliton in mixed coordinate--momentum space, with the coordinate parallel to the layers and the momentum perpendicular to them. The breather dynamics originate from miniband formation, which induces a momentum-dependent phase modulation of the soliton. In the absence of interlayer tunnelling, the breather dynamics disappear and the soliton becomes stationary. These results establish a direct connection between interlayer tunnelling, miniband formation and soliton dynamics, suggesting that breather behavior can provide a signature of interlayer tunnelling in quasi-2D perovskite superlattices.

nlin.PS↗