Interlaced solitons and vortices in coupled DNLS lattices

Cuevas, J.; Hoq, Q.E.; Susanto, Hadi

doi:10.1016/j.physd.2009.09.002

Cited by 12 publications

(19 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Work in this direction was reported in Refs. [100,101,102,103]. As the soliton tails decay fairly rapidly, there may be little difference in the form of the solutions if the ring or torus is large enough, while, as they are made smaller, one may expect curvature effects to come into play.…”

Section: Discussionmentioning

confidence: 99%

Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices

Gorder

Krause

Malomed

et al. 2020

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

We study coupled unstaggered-staggered soliton pairs emergent from a system of two coupled discrete nonlinear Schrödinger (DNLS) equations with the self-attractive on-site self-phasemodulation nonlinearity, coupled by the repulsive cross-phase-modulation interaction, on 1D and 2D lattice domains. These mixed modes are of a "symbiotic" type, as each component in isolation may only carry ordinary unstaggered solitons. While most work on DNLS systems addressed symmetric on-site-centered fundamental solitons, these models give rise to a variety of other excited states, which may also be stable. The simplest among them are antisymmetric states in the form of discrete twisted solitons, which have no counterparts in the continuum limit. In the extension to 2D lattice domains, a natural counterpart of the twisted states are vortical solitons. We first introduce a variational approximation (VA) for the solitons, and then correct it numerically to construct exact stationary solutions, which are then used as initial conditions for simulations to check if the stationary states persist under time evolution. Twocomponent solutions obtained include (i) 1D fundamental-twisted and twisted-twisted soliton pairs, (ii) 2D fundamental-fundamental soliton pairs, and (iii) 2D vortical-vortical soliton pairs. We also highlight a variety of other transient dynamical regimes, such as breathers and amplitude death. The findings apply to modeling binary Bose-Einstein condensates, loaded in a deep lattice potential, with identical or different atomic masses of the two components, and arrays of bimodal optical waveguides. keywords: discrete nonlinear Schrödinger equations; unstaggered-staggered lattice; variational 1 arXiv:2003.00591v1 [nlin.PS] 1 Mar 2020 approximation; solitons 1 IntroductionDiscrete nonlinear Schrödinger (DNLS) equations provide models for a great variety of physical systems [1]. A well-known implementation of the basic DNLS equation is provided by arrays of transversely coupled optical waveguides, as predicted in [2] and realized experimentally, in various optical settings [3,4,5,6]. A comprehensive review of nonlinear optics in discrete settings was given by Ref. [7]. Another realization of the DNLS equation in provided by Bose-Einstein condensates (BECs) loaded into deep optical-lattice potentials, which split the condensate into a chain of droplets trapped in local potential wells, which are tunnel-coupled across the potential barriers between them [8,9]. In the tight-binding approximation, this setting is also described by the DNLS version of the Gross-Pitaevskii (GP) equation [10,11,12,13,14].One-dimensional (1D) DNLS equations with self-attractive and self-repulsive on-site nonlinearity generate localized modes of unstaggered and staggered types, respectively. In the latter case, the on-site amplitudes alternate between adjacent sites of the lattice [1]. In the continuum limit, the unstaggered discrete solitons carry over into regular ones, while the staggered solitons correspond to gap solitons, which are supported...

show abstract

Section: Discussionmentioning

confidence: 99%

Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices

Gorder

Krause

Malomed

et al. 2020

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

show abstract

“…[36,38]. Generalizations of such states in two-dimensional waveguide arrays with the formation of vortex-bright states [39] or of genuinely discrete variants thereof [44] would also be an exciting theme for future investigations.…”

Section: Conclusion and Future Challengesmentioning

confidence: 96%

Dark-bright gap solitons in coupled-mode one-dimensional saturable waveguide arrays

et al. 2011

View full text Add to dashboard Cite

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 that 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 nonsymbiotic 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.

show abstract

“…Our fundamental model will be that of the two coupled DNLS equations (see e.g. [16,29,6]) of the form:…”

Section: General Theorymentioning

confidence: 99%

Intrinsic localized modes in coupled DNLS equations from the anti-continuum limit

Susanto

Rothos

2016

Mathematics and Computers in Simulation

Self Cite

View full text Add to dashboard Cite

In the present work, we generalize earlier considerations for intrinsic localized modes consisting of a few excited sites, as developed in the one-component discrete nonlinear Schrödinger equation model, to the case of two-component systems. We consider all the different combinations of "up" (zero phase) and "down" (π phase) site excitations and are able to compute not only the corresponding existence curves, but also the eigenvalue dependence of the small eigenvalues potentially responsible for instabilities, as a function of the nonlinear parameters of the model representing the self/cross phase modulation in optics and the scattering length ratios in the case of matter waves in optical lattices. We corroborate these analytical predictions by means of direct numerical computations. We infer that all the modes which bear two adjacent nodes with the same phase are unstable in the two component case and the only solutions that may be linear stable are ones where each set of adjacent nodes, in each component is out of phase.

show abstract

Interlaced solitons and vortices in coupled DNLS lattices

Cited by 12 publications

References 46 publications

Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices

Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices

Dark-bright gap solitons in coupled-mode one-dimensional saturable waveguide arrays

Intrinsic localized modes in coupled DNLS equations from the anti-continuum limit

Contact Info

Product

Resources

About