Search arXivSearch

arXiv · nlin/0409042

Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media

Abstract

We demonstrate that two-dimensional two-component bright solitons of an annular shape, carrying vorticities $(m,\pm m)$ in the components, may be stable in media with the cubic-quintic nonlinearity, including the \textit{hidden-vorticity} (HV) solitons of the type $(m,-m)$, whose net vorticity is zero. Stability regions for the vortices of both $(m,\pm m)$ types are identified for $m=1$, 2, and 3, by dint of the calculation of stability eigenvalues, and in direct simulations. A novel feature found in the study of the HV solitons is that their stability intervals never reach the (cutoff) point at which the bright vortex carries over into a dark one, hence dark HV solitons can never be stable, contrarily to the bright ones. In addition to the well-known symmetry-breaking (\textit{external}) instability, which splits the ring soliton into a set of fragments flying away in tangential directions, we report two new scenarios of the development of weak instabilities specific to the HV solitons. One features \textit{charge flipping}, with the two components exchanging the angular momentum and periodically reversing the sign of their spins. The composite soliton does not split in this case, therefore we identify such instability as an \textit{intrinsic} one. Eventually, the soliton splits, as weak radiation loss drives it across the border of the ordinary strong (external) instability. Another scenario proceeds through separation of the vortex cores in the two components, each individual core moving toward the outer edge of the annular soliton. After expulsion of the cores, there remains a zero-vorticity breather with persistent internal vibrations.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, C. Denz, F. Lederer. 2004-09-21. Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media. https://doi.org/10.1103/physreve.71.026615

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

KEEP EXPLORING

Related papers

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

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