Search arXiv⌕ Search

arXiv · nlin/0507047

Propagation of Discrete Solitons in Inhomogeneous Networks

Abstract

In many physical applications solitons propagate on supports whose topological properties may induce new and interesting effects. In this paper, we investigate the propagation of solitons on chains with a topological inhomogeneity generated by the insertion of a finite discrete network on the chain. For networks connected by a link to a single site of the chain, we derive a general criterion yielding the momenta for perfect reflection and transmission of traveling solitons and we discuss solitonic motion on chains with topological inhomogeneities.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

R. Burioni, D. Cassi, P. Sodano, A. Trombettoni, A. Vezzani. 2005-07-22. Propagation of Discrete Solitons in Inhomogeneous Networks. https://doi.org/10.1063/1.2049147

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

KEEP EXPLORING

Related papers

Superregular solitonic solutions of the defocusing nonlocal nonlinear Schrodinger equation and their novel perspectives

Previous studies have indicated that the local defocusing nonlinear Schrödinger equation (NLSE) is modulationally stable. Therefore, superregular solitonic solutions characterizing the nonlinear evolution of modulational instability under weak localized perturbations do not exist. In this work, we study the nonlinear stage of the modulation instability of a condensate in the framework of the defocusing nonlocal NLSE. By using the dressing method and Joukowski transformation, we systematically derive the general $N$-solitonic solution of the defocusing nonlocal NLSE, and the explicit expressions for one-solitonic, two-solitonic and superregular two-solitonic solutions are provided. Then dynamics of these solutions is also examined. We find that these solutions show a much wider variety than those in the local NLSE, such as the one solitonic solution composed of two interacting wave components and the two-solitonic solution containing four wave components. Finally, the accuracy and noise robustness of the analytical solutions are confirmed by numerical simulations. Such results advance the theory of superregular solitonic solutions in nonlocal systems and offer new physical understanding of wave propagation in nonlocal nonlinear media.

nlin.PS↗

Synchronization transitions in ensembles of active particles with distance-dependent higher-order interactions

Higher-order interactions are ubiquitous in biological systems and can be used to better describe the ensemble dynamics of self-propelled particles. To this end, this article investigates a Vicsek-Kuramoto model with distance-dependent higher-order interactions and obtains analytical results, albeit under certain assumptions, that characterize its collective dynamics. Subsequently, these are validated through simulations of the system equations, demonstrating both continuous and explosive transitions between the asynchronous and synchronous collective states. Further numerical results also reveal that short-range interactions and tightly clustered initial states can lead to deviations from the theoretical predictions, whereas the latter can be offset by increasing the common self-propulsion velocity. These results offer insights into a broad class of active matter systems with higher-order interactions, and provide a framework for designing and utilizing them for specific applications.

nlin.PS↗

A Christov Integrating Factor Method for Approximating Rational PDE Solutions

Rational solutions of partial differential equations (PDEs) are notoriously difficult to approximate via spectral Fourier methods due to their algebraically slow decay rate. In this work we discuss approximating rational PDE solutions in a basis of orthogonal functions known as the Christov functions, allowing for the computation of its spectrum via the fast Fourier transform. An explicit fourth-order integrating factor method is derived. The effectiveness of the method is tested on several nonlinear PDEs. Relative to a straightforward pseudo-spectral approximation, the integrating factor method supports larger regions of stability resulting in a more efficient scheme.

nlin.PS↗