Interlaced solitons and vortices in coupled DNLS lattices

School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom
Physica D Nonlinear Phenomena (Impact Factor: 1.64). 01/2009; 238(22):2216-2226. DOI: 10.1016/j.physd.2009.09.002
Source: arXiv


In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one component, namely interlaced solitons. In the anti-continuum limit of uncoupled sites, these are waveforms whose one component has support where the other component does not. We illustrate systematically how one can combine dynamically stable unary patterns to create stable ones for the binary case of two-components. For the one-dimensional setting, we provide a detailed theoretical analysis of the existence and stability of these waveforms, while in higher dimensions, where such analytical computations are far more involved, we resort to corresponding numerical computations. Lastly, we perform direct numerical simulations to showcase how these structures break up, when they are exponentially or oscillatorily unstable, to structures with a smaller number of participating sites.

Download full-text


Available from: Qazi Hoq, Nov 26, 2014
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In the present work, we numerically explore the existence and stability properties of different types of configurations of dark-bright solitons, dark-bright soliton pairs and pairs of dark-bright and dark solitons in discrete settings, starting from the anti-continuum limit. We find that while single discrete dark-bright solitons have similar stability properties to discrete dark solitons, their pairs may only be stable if the bright components are in phase and are always unstable if the bright components are out of phase. Pairs of dark-bright solitons with dark ones have similar stability properties as individual dark or dark-bright ones. Lastly, we consider collisions between dark-bright solitons and between a dark-bright one and a dark one. Especially in the latter and in the regime where the underlying lattice structure matters, we find a wide range of potential dynamical outcomes depending on the initial soliton speed. Comment: To be published in Physica D
    Preview · Article · Dec 2010 · Physica D Nonlinear Phenomena
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Non-time reversible phonobreathers are non-linear waves that can transport energy in coupled oscillator chains by means of a phase-torsion mechanism. In this paper, the stability properties of these structures have been considered. It has been performed an analytical study for low-coupling solutions based upon the so called {\em multibreather stability theorem} previously developed by some of the authors [Physica D {\bf 180} 235]. A numerical analysis confirms the analytical predictions and gives a detailed picture of the existence and stability properties for arbitrary frequency and coupling.
    Full-text · Article · Jan 2011 · Journal of Physics A Mathematical and Theoretical
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In the present work, we consider the dynamics of dark solitons as one mode of a defocusing photorefractive lattice coupled with bright solitons as a second mode of the lattice. Our investigation is motivated by an experiment which illustrates that such coupled states can exist with both components in the first gap of the linear band spectrum. This finding is further extended by the examination of different possibilities from a theoretical perspective, such as symbiotic ones where the bright component is supported by states of the dark component in the first or second gap, or non-symbiotic ones where the bright soliton is also a first-gap state coupled to a first or second gap state of the dark component. While the obtained states are generally unstable, these instabilities typically bear fairly small growth rates which enable their observation for experimentally relevant propagation distances.
    Preview · Article · Apr 2011 · Physical Review A
Show more