Existence of an internal quasimode for a sine-Gordon soliton

Boesch, R.; Willis, C. R.

doi:10.1103/physrevb.42.2290

Cited by 37 publications

(68 citation statements)

References 13 publications

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“…The SG quasimode can be excited as an initial condition by deforming the slope or the width of the kink as an initial condition as we did in our derivations and simulations in Ref. [1] and as the authors of Ref. [3] did in their second numerical investigation which we discuss in the next section.…”

Section: First Numerical Investigationmentioning

confidence: 99%

“…[1] that we actually solved for the SG quasimode in Ref. [1]. We need these rigorous equations in order to contrast them with the two CV equations of motion for the kink momentum P (t) and width of the kink l(t) which form the basis of their theoretical analysis of our equations of motion and which we repeat below in Eqs.…”

Section: Equations Of Motion For the Sg Quasimodementioning

confidence: 99%

“…[1] we proved the continuum Sine-Gordon (SG) equation has a long lived quasimode whose frequency from simulation is ω s = (1.004 ± 0.001) Γ 0 (where Γ 0 is the frequency of the lower band edge in units where the speed of sound c = 1) and whose lifetime from simulation is (1/τ s ) = (0.003 ± 0.001) Γ 0 . We used a rigorous projection operator collective variable (CV) formalism for nonlinear Klein-Gordon equations derived in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…[3] the authors performed two numerical investigations for the SG in which they assert "show that neither intrinsic internal modes nor quasimodes exist in contrast to previous results" referring to Ref. [1]. In Secs.III and IV we analyze their two numerical investigations in detail and prove their first numerical investigation could not possible observe the quasimode in principle and that their second numerical investigations actually observes the SG quasimode at the beginning of their simulation.…”

Section: Introductionmentioning

confidence: 99%

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Comment on “Existence of internal modes of sine-Gordon kinks”

Willis

2006

Phys. Rev. E

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In Ref. [1] [Phys. Rev. B. 42, 2290Rev. B. 42, (1990] we used a rigorous projection operator collective variable formalism for nonlinear Klein-Gordon equations to prove the continuum Sine-Gordon (SG) equation has a long lived quasimode whose frequency ωs= 1.004 Γ0 is in the continuum just above the lower phonon band edge with a lifetime (1/τs ) = 0.0017 Γ0. We confirmed the analytic calculations by simulations which agreed very closely with the analytic results. In Ref.[3] [Phys. Rev. E. 62, R60 (2000)] the authors performed two numerical investigations which they asserted "show that neither intrinsic internal modes nor quasimodes exist in contrast to previous results." In this paper we prove their first numerical investigation could not possibly observe the quasimode in principle and their second numerical investigation actually demonstrates the existence of the SG quasimode. Our analytic calculations and verifying simulations were performed for a stationary Sine-Gordon soliton fixed at the origin. Yet the authors in Ref.[3] state the explanation of our analytic simulations and confirming simulations are due to the Doppler shift of the phonons emitted by our stationary Sine-Gordon soliton which thus has a zero Doppler shift.

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Section: First Numerical Investigationmentioning

confidence: 99%

Section: Equations Of Motion For the Sg Quasimodementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Comment on “Existence of internal modes of sine-Gordon kinks”

Willis

2006

Phys. Rev. E

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“…Some authors [12,13,14,15,16,17,18] have claimed that they have found an internal quasimode described as a long-lived oscillation of the width of the sine-Gordon soliton.…”

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confidence: 99%

Internal modes of sine-Gordon solitons in the presence of spatiotemporal perturbations

2002

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We investigate the dynamics of the sine-Gordon solitons perturbed by spatiotemporal external forces. We prove the existence of internal (shape) modes of sine-Gordon solitons when they are in the presence of inhomogeneous space-dependent external forces, provided some conditions (for these forces) hold. Additional periodic time-dependent forces can sustain oscillations of the soliton width. We show that, in some cases, the internal mode even can become unstable, causing the soliton to decay in an antisoliton and two solitons. In general, in the presence of spatiotemporal forces the soliton behaves as a deformable (non-rigid) object. A soliton moving in an array of inhomogeneities can also present sustained oscillations of its width. There are very important phenomena (like the soliton-antisoliton collisions) where the existence of internal modes plays a crucial role.

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Transient soliton dynamics in perturbation fields

Majerníková

Drobný

1992

Z. Physik B - Condensed Matter

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Existence of an internal quasimode for a sine-Gordon soliton

Cited by 37 publications

References 13 publications

Comment on “Existence of internal modes of sine-Gordon kinks”

Comment on “Existence of internal modes of sine-Gordon kinks”

Internal modes of sine-Gordon solitons in the presence of spatiotemporal perturbations

Transient soliton dynamics in perturbation fields

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