Localized solutions for a nonlocal discrete NLS equation

Ben, Roberto; Aké, Luis Alberto Cisneros; Minzoni, Antonmaria A.; Panayotaros, Panayotis

doi:10.1016/j.physleta.2015.04.012

Cited by 10 publications

(28 citation statements)

References 20 publications

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“…Along the years the DNLS has been examined for several lattices and various dimensionalities, and under a variety of conditions ranging from disorder in the on-site energies [10][11][12] , effect of nonlinear impurities [13][14][15][16][17][18] , nonlocal effects 19 , disorder of the nonlinear parameter 20 , and long-range effects 21 . Perhaps the most striking feature observed is the robustness of the discrete soliton, under many of these conditions.…”

Section: Introductionmentioning

confidence: 99%

Seltrapping in flat band lattices with nonlinear disorder

Rivas

Molina

2020

Sci Rep

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We study the selftrapping properties of an initially localized excitation in several flat band lattices, in the presence of nonlinear (Kerr) disorder. In the weak nonlinearity regime, the dynamics is controlled by the degeneracy of the bands leading to a linear form of selftrapping. In the strong nonlinearity regime, the dynamics of the excitations depends strongly on the local environment around the initial excitation site that leads to a highly fluctuating selfrapping profile. It is shown that the spreading of the wavefunction in the presence of random nonlinearity, is always completely inhibited about fifty percent of all cases. The role of degeneracy associated with the flatbands is explained with the help of the n-simplex system, which can be solved in closed form.

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Section: Introductionmentioning

confidence: 99%

Seltrapping in flat band lattices with nonlinear disorder

Rivas

Molina

2020

Sci Rep

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“…Finally, besides our original motivation of establishing a connection between solutions of the Klein-Gordon model with those of the corresponding dNLS normal form, we stress that the study of discrete solitons in beyond nearest neighbor 1-dimensional dNLS models has received some attention in the recent literature [6,7,20]. We expect that the results we are going to present can provide some additional insight on this and similar topics, as, e.g., for discrete solitons in zigzag dNLS models [10].…”

Section: Theoretical Setup and Principal Resultsmentioning

confidence: 99%

On the nonexistence of degenerate phase-shift discrete solitons in a dNLS nonlocal lattice

Penati

Sansottera

Paleari

et al. 2018

Physica D: Nonlinear Phenomena

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We consider a one-dimensional discrete nonlinear Schrödinger (dNLS) model featuring interactions beyond nearest neighbors. We are interested in the existence (or nonexistence) of phase-shift discrete solitons, which correspond to four-sites vortex solutions in the standard two-dimensional dNLS model (square lattice), of which this is a simpler variant. Due to the specific choice of lengths of the inter-site interactions, the vortex configurations considered present a degeneracy which causes the standard continuation techniques to be non-applicable.In the present one-dimensional case, the existence of a conserved quantity for the soliton profile (the so-called density current), together with a perturbative construction, leads to the nonexistence of any phase-shift discrete soliton which is at least C 2 with respect to the small coupling ǫ, in the limit of vanishing ǫ. If we assume the solution to be only C 0 in the same limit of ǫ, nonexistence is instead proved by studying the bifurcation equation of a Lyapunov-Schmidt reduction, expanded to suitably high orders. Specifically, we produce a nonexistence criterion whose efficiency we reveal in the cases of partial and full degeneracy of approximate solutions obtained via a leading order expansion.

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“…They also arise by natural ways in certain physics models; see, for example, the discussion before formula (2.20) of [3]. The function σ → KMS ρ (e iσ ) decreases on [0, π] and increases on [π, 2π].…”

Section: Examplesmentioning

confidence: 99%

Eigenvectors of Hermitian Toeplitz matrices with smooth simple-loop symbols

Bogoya

Böttcher

Grudsky

et al. 2016

Linear Algebra and its Applications

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The paper is devoted to the structure and the asymptotics of the eigenvector matrix of Hermitian Toeplitz matrices with moderately smooth symbols which trace out a simple loop on the real line. The results extend existing results on banded Toeplitz matrices to full Toeplitz matrices with temperate decay of the entries in the first row and column. We establish formulas for both the exact and the asymptotic computation of arbitrarily prescribed individual components of arbitrarily prescribed individual eigenvectors. These formulas are in terms of the Wiener-Hopf factorization of a function which depends solely on the symbol and the corresponding eigenvalue or even only on an approximation to this eigenvalue. The paper does not aim at providing numerical algorithms. Its main purpose is rather to reveal the structure underneath the eigenvectors, which are shown to be the sum of two harmonics and certain edge corrections. (J.M. Bogoya), aboettch@mathematik.tu-chemnitz.de (A. Böttcher), grudsky@math.cinvestav.mx (S.M. Grudsky), maximenko@esfm.ipn.mx (E.A. Maximenko).

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Localized solutions for a nonlocal discrete NLS equation

Cited by 10 publications

References 20 publications

Seltrapping in flat band lattices with nonlinear disorder

Seltrapping in flat band lattices with nonlinear disorder

On the nonexistence of degenerate phase-shift discrete solitons in a dNLS nonlocal lattice

Eigenvectors of Hermitian Toeplitz matrices with smooth simple-loop symbols

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