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Full-Text Articles in Physical Sciences and Mathematics
Interlaced Solitons And Vortices In Coupled Dnls Lattices, J Cuevas, Qe Hoq, H Susanto, Pg Kevrekidis
Interlaced Solitons And Vortices In Coupled Dnls Lattices, J Cuevas, Qe Hoq, H Susanto, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
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 …
Existence, Stability, And Dynamics Of Bright Vortices In The Cubic-Quintic Nonlinear Schr¨Odinger Equation, R M. Caplan, R Carretero-Gonzalez, Pg Kevrekidis
Existence, Stability, And Dynamics Of Bright Vortices In The Cubic-Quintic Nonlinear Schr¨Odinger Equation, R M. Caplan, R Carretero-Gonzalez, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We study the existence and azimuthal modulational stability of vortices in the two-dimensional (2D) cubic-quintic nonlinear Schr¨odinger (CQNLS) equation. We use a variational approximation (VA) based on an asymptotically derived ansatz, seeding the result as an initial condition into a numerical optimization routine. Previously known existence bounds for the vortices are recovered by means of this approach. We study the azimuthal modulational stability of the vortices by freezing the radial direction of the Lagrangian functional of the CQNLS, in order to derive a quasi-1D azimuthal equation of motion. A stability analysis is then done in the Fourier space of the …
Vortex Solutions Of The Discrete Gross-Pitaevskii Equation Starting From The Anti-Continuum Limit, J Cuevas, G James, Pg Kevrekidis, Kjh Law
Vortex Solutions Of The Discrete Gross-Pitaevskii Equation Starting From The Anti-Continuum Limit, J Cuevas, G James, Pg Kevrekidis, Kjh Law
Mathematics and Statistics Department Faculty Publication Series
In this paper, we consider the existence, stability and dynamical evolution of dark vortex states in the two-dimensional defocusing discrete nonlinear Schrödinger model, a model of interest both to atomic physics and to nonlinear optics. Our considerations are chiefly based on initializing such vortex configurations at the anti-continuum limit of zero coupling between adjacent sites, and continuing them to finite values of the coupling. Systematic tools are developed for such continuations based on amplitude-phase decompositions and explicit solvability conditions enforcing the vortex phase structure. Regarding the linear stability of such nonlinear waves, we find that in a way reminiscent of …