Discreteness effects on a sine-Gordon breather

Boesch, R.; Peyrard, Michel

doi:10.1103/physrevb.43.8491

Cited by 40 publications

(23 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If these length scales are very different from each other the perturbed dynamics can support solitonlike or breatherlike excitations. The motion of these excitations can be described by a collective variable approach [3,4]. On the other hand, if the length scales are comparable localized excitations break up or dissipate into radiation even for relatively small strength of the perturbation.…”

mentioning

confidence: 99%

Sine-Gordon kink-antikink generation on spatially periodic potentials

et al. 1992

View full text Add to dashboard Cite

A spatially periodic perturbation can lead to a breakup of large-amplitude sine-Gordon breathers into kink and anti kink solutions, each oscillating around a minimum of the perturbing potential. This behavior can be understood by studying the effective potential experienced by the breather (bound kink-antikink) or the (free) kink-antikink solution as long as kink and antikink are sufficiently far apart. The resulting kinks and antikinks move independently and nearly radiationlessly in the presence of the perturbation and can travel arbitrarily far for sufficiently large initial kinetic energy. Upon interacting with each other they are strongly affected by the perturbation, lose energy by radiating, and can end in a bound state having the character of a distorted breather.PACS numbers: 03.40. Kf, 61.70.Ga Adding spatial disorder to completely integrable nonlinear dynamics like the one governed by the nonlinear Schrodinger (NLS) equation or the sine-Gordon (SG) equation leads to a variety of novel effects having practical relevance [1]. Competition of the length scales introduced by the perturbation and by the nonlinearity is one example we have studied recently [2]. If these length scales are very different from each other the perturbed dynamics can support solitonlike or breatherlike excitations. The motion of these excitations can be described by a collective variable approach [3,4]. On the other hand, if the length scales are comparable localized excitations break up or dissipate into radiation even for relatively small strength of the perturbation. This behavior has been observed in the case of the SG equation[2] as well as for the NLS equation [5].Another class of effects induced by spatially periodic perturbations can be observed in dynamics which allow for topological solitons like the SG equation. Although very many perturbed SG problems have been considered in the literature (see, e.g., [6,7] for reviews), to our best knowledge, only Mkrtchyan and Shmidt [8] and Malomed and Tribelsky [9] have studied the motion of SG kinks under the influence of a cosine potential. In this case kinks (and antikinks) seem to move radiationlessly below a certain velocity threshold. The question arises whether kinks and anti kinks also interact radiationlessly under these circumstances. Finally it is interesting to see under which conditions a breather can break up into a kinkantikink (f{-f{) pair under the perturbation [2].In this Rapid Communication we address the question of how large-amplitude SG breathers behave under the influence of spatially periodic potentials. These potentials include the effects of discreteness as a particular case; they also can be relevant to understand the interaction of domain wall excitations in discrete solid-state and materials science problems governed by SG-like equations of motion, for example, dislocations in a crystal, walls in ferroelectrics or ferromagnets, or discommensurations in superlattices. A breather can be interpreted as a bound f{-f{ state (see a detailed account of the ...

show abstract

mentioning

confidence: 99%

Sine-Gordon kink-antikink generation on spatially periodic potentials

et al. 1992

View full text Add to dashboard Cite

show abstract

“…In this case, the phonon band is very wide and the e ect observed by Boesch and Peyrard [11] cannot take place because 3x b cannot reach the upper phonon band edge. However, an interesting resonance e ect takes place for a large-amplitude breather when 2m 1 x b with a positive integer m becomes greater than the frequency of the lower phonon band edge.…”

Section: Introductionmentioning

confidence: 89%

“…Boesch and Peyrard have shown that the e ect of the increase of breather lifetime [11] takes place at 3x b b x 1a2 . However, since x b does not exceed 1, the e ect can be observed only for h b 1a 2 p % 0X71.…”

Section: Frenkel±kontorova Model and Sine-gordon Equationmentioning

confidence: 99%

“…The resonance between the breather oscillation and the phonons has been investigated for a highly discrete SG system by Boesch and Peyrard [11]. They studied the emission of phonons from breather.…”

Section: Introductionmentioning

confidence: 99%

“…In the course of the oscillation, the breather constantly loses energy and its frequency x b gradually increases. When 3x b becomes greater than the frequency of the upper phonon band edge, the energy emission drops down and the lifetime of the breather drastically increases [11].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations