Mobility of discrete multibreathers in the exciton dynamics of the Davydov model with saturable nonlinearities

Tchameu, J.D. Tchinang; Motcheyo, A.B. Togueu; Tchawoua, Clément

doi:10.1103/physreve.90.043203

Cited by 17 publications

(4 citation statements)

References 43 publications

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“…A generalization of the polaron to solectron, which is the bound state of the crowdion or DB and electron has been proposed () to discuss the peculiarities of electron transport in crystals .…”

Section: Possible Applications Of Discrete Breathersmentioning

confidence: 99%

“…A generalization of the polaron to solectron, which is the bound state of the crowdion or DB and electron has been proposed [55] to discuss the peculiarities of electron transport in crystals [56][57][58][59]. As a future challenge, it is important to search for DB in auxetics, among which are crystals and other discrete nonlinear systems [60][61][62][63][64][65].…”

Section: Papermentioning

confidence: 99%

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Discrete breathers in 2D and 3D crystals

Chetverikov

Velarde

2015

Physica Status Solidi (b)

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Discrete breathers (DB) are spatially localized, large‐amplitude vibrational modes in defect‐free nonlinear lattices. Recent numerical and experimental studies have confirmed that DB exist in crystals. In the present work, we briefly describe the well‐known existence conditions of DB in crystals and present our recent results on DB in 2D crystals such as graphene and graphane and in 3D crystals such as alkali halide crystals and pure metals. The possible role of DB in solid state physics and materials science is discussed. Stroboscopic picture of atomic motions in the vicinity of discrete breather excited in graphene homogeneously strained with ϵxx=0.3, ϵyy=−0.1. Displacements of atoms from the equilibrium lattice positions are multiplied by the factor 4 for clarity. The discrete breather is of high spatial localization, so that only two atoms oscillate with a large amplitude.

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Section: Possible Applications Of Discrete Breathersmentioning

confidence: 99%

Section: Papermentioning

confidence: 99%

Discrete breathers in 2D and 3D crystals

Chetverikov

Velarde

2015

Physica Status Solidi (b)

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“…The discrete versions of the NLS-type Equation ( 1) is increasingly provoking people's interest on account of the biological applications [23][24][25][26][27]. This paper is devoted to the following higher-order integrable discrete NLS (dNLS) equation [11]:…”

Section: Introductionmentioning

confidence: 99%

“…The discrete versions of the NLS‐type Equation () is increasingly provoking people's interest on account of the biological applications [23–27]. This paper is devoted to the following higher‐order integrable discrete NLS (dNLS) equation [11]:

\begin{matrix} right i q_{n, t} & left + \frac{γ}{h^{4}} [(1 + | q_{n} |^{2}) ((1 + | q_{n - 1} |^{2}) q_{n - 2} + (1 + | q_{n + 1} |^{2}) q_{n + 2} - 4 q_{n - 1} - 4 q_{n + 1} + q_{n}^{*} (q_{n + 1}^{2} + q_{n - 1}^{2}) \\ right & left + q_{n} (q_{n - 1}^{*} q_{n + 1} + q_{n - 1} q_{n + 1}^{*})) + 6 q_{n}] + \frac{1}{h^{2}} ((1 + | q_{n} |^{2}) (q_{n + 1} + q_{n - 1}) - 2 q_{n}) = 0 . \end{matrix}

…”

Section: Introductionmentioning

confidence: 99%

Continuum limits for rational, breather solutions, and gauge equivalent model of the generalized discrete nonlinear Schrödinger equation

Huang

Zhang

et al. 2023

Math Methods in App Sciences

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In this paper, we focus on an integrable higher‐order discrete nonlinear Schrödinger (dNLS) equation, which yields the Lakshmanan–Porsezian–Daniel (LPD) equation in the continuum limit. The breather solutions of the higher‐order dNLS are obtained for the first time. We show that the rational solutions and breather solutions of the higher‐order dNLS equation yield the counterparts of the integrable fourth‐order NLS equation under proper continuous limits. Most importantly, we also explore the gauge equivalent equation of the higher‐order dNLS equation from the point of view of the continuous limit theory. We make integrable discretization for the linear spectrum problem of the integrable generalized Heisenberg ferromagnetic equation that is just the gauge equivalent structure of the LPD equation. Compatibility condition of the discrete linear spectrum problem leads to a discrete integrable generalized Heisenberg Ferromagnetic equation. It is revealed that the discrete linear spectrum problem of the discrete integrable generalized ferromagnetic equation converges to the corresponding spectrum problem of the integrable generalized Feisenberg spin model in the continuum limit.In addition, with the help of the method of linear combinations for the conserved fluxes and densities, the conservation laws of the integrable higher‐order dNLS equation converge to the homologous results of the LPD equation.

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