Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · nlin/0209052

Optical soliton solutions of the quintic complex Swift-Hohenberg equation

Adrian Ankiewicz·Ken-ichi Maruno·Nail Akhmediev
View original source ↗Read source document ↗Export metadata ↓

Abstract

Using a direct ansatz approach, we have found a number of zero-velocity analytic solutons of the complex quintic Swift-Hohenberg equation. These find application in assorted optical problems.

Explore related subjects

nlin.PSnlin.AOphysics.optics

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Adrian Ankiewicz, Ken-ichi Maruno, Nail Akhmediev. 2002-09-24. Optical soliton solutions of the quintic complex Swift-Hohenberg equation. https://doi.org/10.1016/s0375-9601(03)00080-x

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

KEEP EXPLORING

Related papers

arXiv2026

Routes to chaos in a mass-conserving two-species reaction-diffusion model

Mass-conserving reaction-diffusion systems with two species correspond to a seemingly simple case where pattern formation occurs under the influence of a conservation law. Here, we first revisit their linear stability behavior and point out that generically two instabilities can occur: a stationary large-scale mass-conserving (Cahn-Hilliard) instability and an instability that combines features of a stationary large-scale non-mass-conserving (Allen-Cahn) instability and a oscillatory large-scale mass-conserving (conserved-Hopf) instability. We term it an Allen-Cahn-Hopf instability. Second, we investigate the nonlinear dynamics for a specific model related to the formation of cell polarization where only a Cahn-Hilliard instability can occur, i.e., all primary bifurcations are stationary. We analyze how secondary and further bifurcations subsequently give rise to various oscillatory states. The emerging rich spectrum of spatiotemporal behavior includes several period-doubling cascades related to different forms of spatial and temporal symmetry breaking. Beside regular states, three types of low-dimensional spatiotemporal chaos occur and involve transitions like fusion and an outer crises. Our results demonstrate the importance of nonlinear interactions in the dynamics of mass-conserving reaction-diffusion systems, and show that even a simple two-species system with primary bifurcations of Cahn-Hilliard type can show complex spatiotemporal behavior.

nlin.PS↗
arXiv2026

Duck hunting with quantum mechanics

We bridge two sides of singular perturbation theory: the classical theory of slow-fast systems and the semi-classical approach to quantum mechanical systems. For a specific but physically important class of dynamical systems, we show that purely classical and exotic objects, so-called canard solutions, are shadows of instantons in the corresponding quantum system. We demonstrate that canard solutions exist in a domain of parameter space whose boundaries are determined by an instanton action. We illustrate our statements analytically for the relevant example, the overdamped Josephson junction, and confirm them numerically. For the Josephson junction, the canard window is the exponentially narrow gap between consecutive Shapiro steps.

nlin.PS↗