Bifurcation of internal solitary wave modes from the essential spectrum

Jones, Christopher K. R. T.

doi:10.1103/physreve.61.3114

Cited by 38 publications

(46 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We believe that the new models here introduced may perhaps be used to such study, in particular in the lines of [20,25,31,36] to check if the semiclassical study goes as in the double sine-Gordon case. Another line of study could be the search of internal modes [19,22,24], which seems to appear after deforming an integrable model [19]. The sine-Gordon model has also been of interest for String Theory, since it seems to be related to the classical string on specific manifolds [40,41].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Classical behavior of deformed sine-Gordon models

Bazeia

Losano

Malbouisson

et al. 2008

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

“…Among the several possibilities of study, the specific investigations on classical, semiclassical and other aspects of sine-Gordon, double sine-Gordon and related models [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39] have motivated us to propose the present study.…”

Section: Introductionmentioning

confidence: 99%

Classical behavior of deformed sine-Gordon models

Bazeia

Losano

Malbouisson

et al. 2008

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…Such effects are often related to the feature that the kinks (topological excitations) in non-integrable KleinGordon models can support vibrational internal modes (IM) [2][3][4][5] and that the energy exchange between the kink's translational and vibrational modes is possible [6][7][8][9][10][11][12][13][14]. For the φ 4 , φ 6 , and φ 8 equations the multibounce resonances in the kink-antikink collisions have been observed and have been attributed to the energy exchange between kink translational and vibrational modes [6- * Electronic address: saadatmand.d@gmail.com † Electronic address: borisovdi@yandex.ru ‡ Electronic address: kevrekid@math.umass.edu § Electronic address: kzhou@ntu.edu.sg ¶ Electronic address: dmitriev.sergey.v@gmail.com 10,[12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Resonant interaction of ϕ4 kink with PT-symmetric perturbation with spatially periodic gain/loss coefficient

Saadatmand

Борисов

Kevrekidis

et al. 2018

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

The resonant interaction of the φ 4 kink with a periodic PT -symmetric perturbation is observed in the frame of the continuum model and with the help of a two degree of freedom collective variable model derived in PRA 89, 010102(R). When the kink interacts with the perturbation, the kink's internal mode is excited with the amplitude varying in time quasiperiodically. The maximal value of the amplitude was found to grow when the kink velocity is such that it travels one period of perturbation in nearly one period of the kink's internal mode. It is also found that the kink's translational and vibrational modes are coupled in a way that an increase in the kink's internal mode amplitude results in a decrease in kink velocity. The results obtained with the collective variable method are in a good qualitative agreement with the numerical simulations for the continuum model. The results of the present study suggest that kink dynamics in open systems with balanced gain and loss can have new features in comparison with the case of conservative systems.

show abstract

“…The features and behaviour of kink internal modes for DSGE, as well as for more general types of the so-called Frenkel-Kontorova (FK) model, have been already studied in very details [2,3,4,5]. The spectrum of linear waves of DSGE around a kink contains either two or one localized mode, depending on the value of parameter λ.…”

mentioning

confidence: 99%

Internal modes in sine-Gordon chain

Prilepsky

Kovalev²

2005

Phys. Rev. E

View full text Add to dashboard Cite

We address the issue of internal modes of a kink of a discrete sine-Gordon equation. The main point of the present study is to elucidate how the antisymmetric internal mode frequency dependence enters the quasicontinuum spectrum of nonlocalized waves. We analyze the internal frequency dependencies as functions of both the number of cites and discreteness parameter and explain the origin of spectrum peculiarity which arises after the frequency dependence of antisymmetric mode returns back to the continuous spectrum at some nonzero value of the intersite coupling.PACS numbers: 63.20.Pw, 63.20.Ry The existence of internal modes is a well known peculiarity of nonintegrable systems [1]: If one linearizes a nonintegrable equation above the static nonlinear solution, then the effective potential of the linear equation obtained appears to be not reflectionless in contrast to the integrable case. The particular example is the existence of internal (shape) modes of kinks in the well known discrete sine-Gordon equation (DSGE). This set of differential-difference equations reads as (in normalized dimensionless units):where u n (t) is the field variable, which can have a multitude of physical meanings [2], λ is a coupling parameter, dot means the time derivative and index n numerates the 1D chain sites. The features and behaviour of kink internal modes for DSGE, as well as for more general types of the so-called Frenkel-Kontorova (FK) model, have been already studied in very details [2,3,4,5]. The spectrum of linear waves of DSGE around a kink contains either two or one localized mode, depending on the value of parameter λ. (We consider the stable kink centered between the chain sites.) The frequencies of these modes lie inside the spectrum gap; the linear spectrum itself is given bywhere ω is the frequency of linear waves and k is the wave number. The lowest (gap edge) frequency is ω = 1 (in the renormalized units). However, up to our knowledge, notwithstanding the great quantity of results none so far has concentrated on the way an internal modes ceases to exist: Only the fact of existence or nonexistence of that mode has been the subject of interest [1,2,3,4,5]. In this paper we focus on the effect entailed by the detachment of the internal mode frequency from the spectrum. So, the question * Electronic address: kovalev@ilt.kharkov.ua

show abstract

Bifurcation of internal solitary wave modes from the essential spectrum

Cited by 38 publications

References 30 publications

Classical behavior of deformed sine-Gordon models

Classical behavior of deformed sine-Gordon models

Resonant interaction of ϕ4 kink with PT-symmetric perturbation with spatially periodic gain/loss coefficient

Internal modes in sine-Gordon chain

Contact Info

Product

Resources

About