Intrinsic Localized Anharmonic Modes at Crystal Edges

Bonart, D.; Mayer, Andreas; Schröder, U.

doi:10.1103/physrevlett.75.870

Cited by 31 publications

(15 citation statements)

References 10 publications

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“…10,30 Recently, much attention has been paid to the gap solitons in nonlinear diatomic lattices. 11,27,[31][32][33][34][35][36][37][38][39][40][41] The concept of the gap solitons was first introduced by Chen and Mills 42 when investigating the nonlinear optical response of superlattices. For a diatomic lattice, the phonon spectrum of the system consists of two branches (acoustic and optical ones), induced by mass or force-constant difference of two kinds of particles.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric gap soliton modes in diatomic lattices with cubic and quartic nonlinearity

Huang

1998

Phys. Rev. B

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Nonlinear localized excitations in one-dimensional diatomic lattices with cubic and quartic nonlinearity are considered analytically by a quasi-discreteness approach. The criteria for the occurence of asymmetric gap solitons (with vibrating frequency lying in the gap of phonon bands) and small-amplitude, asymmetric intrinsic localized modes (with the vibrating frequency being above all the phonon bands) are obtained explicitly based on the modulational instabilities of corresponding linear lattice plane waves. The expressions of particle displacement for all these nonlinear localized excitations are also given. The result is applied to standard two-body potentials of the Toda, Born-Mayer-Coulomb, Lennard-Jones, and Morse type. The comparison with previous numerical study of the anharmonic gap modes in diatomic lattices for the standard two-body potentials is made and good agreement is found.

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Section: Introductionmentioning

confidence: 99%

Asymmetric gap soliton modes in diatomic lattices with cubic and quartic nonlinearity

Huang

1998

Phys. Rev. B

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“…Within the framework of this model and, more generally, for Klein-Gordon lattices, it has recently been recognized that physically realistic setups require consideration of the ILM dynamics in higher spatial dimensions [28][29][30][32][33][34][35][36][37]. In the most straightforward two-dimensional (2D) case, almost all of these studies, with the exception of Refs.…”

Section: Introductionmentioning

confidence: 99%

Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity

2002

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We study the existence and stability of localized states in the discrete nonlinear Schrödinger equation (DNLS) on two-dimensional non-square lattices. The model includes both the nearestneighbor and long-range interactions. For the fundamental strongly localized soliton, the results depend on the coordination number, i.e., on the particular type of the lattice. The long-range interactions additionally destabilize the discrete soliton, or make it more stable, if the sign of the interaction is, respectively, the same as or opposite to the sign of the short-range interaction. We also explore more complicated solutions, such as twisted localized modes (TLM's) and solutions carrying multiple topological charge (vortices) that are specific to the triangular and honeycomb lattices. In the cases when such vortices are unstable, direct simulations demonstrate that they turn into zero-vorticity fundamental solitons.

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“…On the other hand, here we have a translationally invariant system. This then shows that nonlinearity can introduce self-localization [26] in the system. This is an interesting result.…”

Section: A Fully Nonlinear Chain With Alternative Nonlinear Strengthsmentioning

confidence: 80%

Lasers emitting at a wavelength of 0.98 μm, constructed from InGaP/GaAs heterostructures grown by MOCVD method

et al. 1994

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We investigate the effect of a nondegenerate quadratic nonlinear dimeric impurity on the formation of stationary localized states in one-dimensional systems. We also consider the formation of stationary self-localized states in a translationally invariant fully nonlinear system where alternative sites have the same nonlinear strengths. Appropriate ansatze have been chosen for all of the cases which reproduce the known results for special cases. The connection of the stability of a state to its energy is presented graphically. † Permanent address:

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Intrinsic Localized Anharmonic Modes at Crystal Edges

Cited by 31 publications

References 10 publications

Asymmetric gap soliton modes in diatomic lattices with cubic and quartic nonlinearity

Asymmetric gap soliton modes in diatomic lattices with cubic and quartic nonlinearity

Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity

Lasers emitting at a wavelength of 0.98 μm, constructed from InGaP/GaAs heterostructures grown by MOCVD method

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