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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 …
Lyapunov-Schmidt Reduction Algorithm For Three-Dimensional Discrete Vortices, M Lukas, D Pelinovsky, Pg Kevrekidis
Lyapunov-Schmidt Reduction Algorithm For Three-Dimensional Discrete Vortices, M Lukas, D Pelinovsky, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We address the persistence and stability of three-dimensional vortex configurations in the discrete nonlinear Schrödinger equation and develop a symbolic package based on Wolfram’s MATHEMATICA for computations of the Lyapunov–Schmidt reduction method. The Lyapunov–Schmidt reduction method is a theoretical tool which enables us to study continuations and terminations of the discrete vortices for small coupling between lattice nodes as well as the spectral stability of the persistent configurations. The method was developed earlier in the context of the two-dimensional lattice and applied to the onsite and offsite configurations (called the vortex cross and the vortex cell) by using semianalytical computations …