Dark–antidark solitons in waveguide arrays with alternating positive–negative couplings

Auditore, Aldo; Conforti, Matteo; Angelis, C. De; Aceves, Alejandro B.

doi:10.1016/j.optcom.2013.01.068

Cited by 10 publications

(1 citation statement)

References 21 publications

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“…Earlier experimental work on binary arrays has already shown the formation of discrete gap solitons [MMS + 04]. Three of the many novel examples that have been recently considered are: a dielectric metallic waveguide array [ACDAA13,AACDA13]; an array of vertically displaced binary waveguide arrays with longitudinally modulated effective refractive index [MLB14], and arrays of coupled parity-time (PT ) nanoresonators [LT13]. We also constructed bi-frequency solutions of the form (1.5) in the Dirac-type models with the PT -symmetry which arise in nonlinear optics in the model describing arrays of optical fibers with gain-loss behavior [CMKS + 16b].…”

Section: Introductionmentioning

confidence: 99%

Spectral stability of bi-frequency solitary waves in Soler and Dirac-Klein-Gordon models

Boussïd¹,

Comech²

2018

Communications on Pure &Amp; Applied Analysis

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We construct bi-frequency solitary waves of the nonlinear Dirac equation with the scalar self-interaction, known as the Soler model (with an arbitrary nonlinearity and in arbitrary dimension) and the Dirac-Klein-Gordon with Yukawa self-interaction. These solitary waves provide a natural implementation of qubit and qudit states in the theory of quantum computing.We show the relation of ±2ωi eigenvalues of the linearization at a solitary wave, Bogoliubov SU(1, 1) symmetry, and the existence of bi-frequency solitary waves. We show that the spectral stability of these waves reduces to spectral stability of usual (one-frequency) solitary waves. To Vladimir Georgiev on the occasion of his 60th birthday1 IntroductionThe Soler model [Iva38, Sol70] is the nonlinear Dirac equation with the minimal scalar self-coupling,where f is a continuous real-valued function with f (0) = 0. Above,ψ = ψ * β, with ψ * the hermitian conjugate. This is one of the main models of the nonlinear Dirac equation, alongside with its own onedimensional analogue, the Gross-Neveu model [GN74, LG75], and with the massive Thirring model [Thi58]. Above, the Dirac operator is given bywith α j (1 ≤ j ≤ n) and β mutually anticommuting self-adjoint matrices such that D 2 m = −∆ + m 2 . All these models are hamiltonian, U(1)-invariant, and relativistically invariant. The classical field ψ could be quantized (see e.g. [LG75]).The Soler model shares the symmetry features with its more physically relevant counterpart, Dirac-Klein-Gordon system (the Dirac equation with the Yukawa self-interaction, which is also based on the quantityψψ):

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