Phonon emission from a discrete sine-Gordon breather

Shigenari, Takeshi; Abe, Kohji; Vasiliev, Aleksey A.; Miroshnichenko, Andrey E.

doi:10.1016/s0927-0256(00)00105-1

Cited by 4 publications

(9 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where u n is now the displacement of the n th particle from an initial point of coordinate x = nh and h is the discreteness parameter that controls the lattice spacing [14].…”

Section: Frenkel-kontorova Model and The Discrete Sg Equationmentioning

confidence: 99%

“…) 2019/20 [14]. This discrete SG equation was introduced by Frenkel & Kontorova in 1938 where they explored crystal dislocations.…”

Section: Frenkel-kontorova Model and The Discrete Sg Equationmentioning

confidence: 99%

“…where 0 ≤ κ ≤ π is the wave number and ω κ is the associated frequency [14]. Similar to the continuum case phonons in 3.1, equation (6.7) represents plane waves of small amplitude, and (6.8) is the dispersion relation between the wave number κ and the frequency ω κ of the phonons.…”

Section: Linearised Discrete Sg Equationmentioning

confidence: 99%

See 2 more Smart Citations

Solitons: Kinks, Collisions and Breathers

Sickotra¹

2021

Preprint

View full text Add to dashboard Cite

In this report, the various 1D single soliton and multi-soliton solutions of the Sine-Gordon equation are explored. First the topological kink solitons and their properties for the Sine-Gordon, as well as the φ 4 model are investigated. This includes energy and momentum conservation laws for both models, as well as static kinks and antikinks. The Bogomol'nyi equation and the importance of Lorentz invariance are also discussed. Then in the second half, the focus is on Sine-Gordon multi-kink solutions, which are found by a separation of variables method rather than using inverse scattering or Bäcklund transforms. These kink-kink and kink-antikink collisions are explained by considering topological charges and interaction energies. The special bound state dynamical breather soliton is obtained and properties such as the binding energy of the breather are presented. Following this, the Frenkel-Kontorova model is explored, leading to the discrete Sine-Gordon model and the introduction of discrete breathers.

show abstract

“…where u n is now the displacement of the n th particle from an initial point of coordinate x = nh and h is the discreteness parameter that controls the lattice spacing [14].…”

Section: Frenkel-kontorova Model and The Discrete Sg Equationmentioning

confidence: 99%

“…) 2019/20 [14]. This discrete SG equation was introduced by Frenkel & Kontorova in 1938 where they explored crystal dislocations.…”

Section: Frenkel-kontorova Model and The Discrete Sg Equationmentioning

confidence: 99%

See 1 more Smart Citation

Solitons: Kinks, Collisions and Breathers

Sickotra¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Although exact time-periodic space-localized solutions are absent in the FK model, 8 numerical simulations 9,10 show that in the FK model the sG breathers survive, and, although lose energy due to resonances of odd multiples to the breather frequency with phonon frequencies, have their lifetime long enough even in the case of strong discreteness ͑10 4 -10 5 periods when the third harmonic to its frequency is greater than the upper phonon band edge͒. 9 In the case of weak discreteness the losses of energy are hardly perceptible.…”

Section: Introductionmentioning

confidence: 99%

“…9 In the case of weak discreteness the losses of energy are hardly perceptible. 10 In connection with studying real physical quasi-1D systems such as long Josephson junctions and quasi-1D ferromagnets there emerged many works treating behavior of sG breathers under action of perturbations breaking exact integrability: dissipative and diverse conservative terms ͑see Ref. [11][12][13], and references therein͒.…”

Section: Introductionmentioning

confidence: 99%

Survival condition for low-frequency quasi-one-dimensional breathers in a two-dimensional strongly anisotropic crystal

Savin¹,

Zubova

Manevitch

2005

Phys. Rev. B

View full text Add to dashboard Cite

We investigate a two-dimensional ͑2D͒ strongly anisotropic crystal ͑2D SAC͒ on substrate: 2D system of coupled linear chains of particles with strong intrachain and weak interchain interactions, each chain being subjected to the sine background potential. Nonlinear dynamics of one of these chains when the rest of them are fixed is reduced to the well known Frenkel-Kontorova ͑FK͒ model. Depending on strengh of the substrate, the 2D SAC models a variety of physical systems: polymer crystals with identical chains having light side groups, an array of inductively coupled long Josephson junctions, anisotropic crystals having light and heavy sublattices. Continuum limit of the FK model, the sine-Gordon ͑sG͒ equation, allows two types of soliton solutions: topological solitons and breathers. It is known that the quasi-one-dimensional topological solitons can propagate also in a chain of 2D system of coupled chains and even in a helix chain in a three-dimensional model of polymer crystal. In contrast to this, numerical simulation shows that the long-living breathers inherent to the FK model do not exist in the 2D SAC with weak background potential. The effect changes scenario of kink-antikink collision with small relative velocity: at weak background potential the collision always results only in intensive phonon radiation while kink-antikink recombination in the FK model results in long-living low-frequency sG breather creation. We found the survival condition for breathers in the 2D SAC on substrate depending on breather frequency and strength of the background potential. The survival condition bears no relation to resonances between breather frequency and frequencies of phonon band-contrary to the case of the FK model.

show abstract

Soliton Collisions

Kevrekidis

2014

Nonlinear Systems and Complexity

View full text Add to dashboard Cite

Phonon emission from a discrete sine-Gordon breather

Cited by 4 publications

References 20 publications

Solitons: Kinks, Collisions and Breathers

Solitons: Kinks, Collisions and Breathers

Survival condition for low-frequency quasi-one-dimensional breathers in a two-dimensional strongly anisotropic crystal

Soliton Collisions

Contact Info

Product

Resources

About