Dynamics of the Davydov–Scott soliton with location or velocity mismatch of its high-frequency component

Blyakhman, L.G.; Gromov, E. M.; Onosova, I. V.; Tyutin, V. V.

doi:10.1016/j.physleta.2017.02.043

Cited by 2 publications

(3 citation statements)

References 17 publications

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“…The dependence of 2 on parameter of nonlinearity-to-dispersion ratio, / , for the two-component soliton (4) is plotted in fig.1. For / = 1, the oscillation frequency from (14) is = 2�2/15/ 2 and coincides with the frequency of oscillations of the HF component in the DS (3), which was obtained earlier in [20]. For / = 3, the oscillation frequency from (14), = 4 �6/35 2 ⁄ , corresponds to the HF oscillation frequency in the soliton (6).…”

Section: Oscillations Of a Perturbed Solitonsupporting

confidence: 83%

“…where 𝛥 is an arbitrary width of the HF component of the soliton, and 𝑉 = (4𝛾 𝛥 2 ⁄ − 𝐴 2 𝛥 2 )/(2𝑉 SIN ) is its soliton's velocity. For a perturbed state of this soliton, oscillations of the HF component with respect to its LF counterpart, originally displayed in [20].…”

Section: The Coupled Linear-schrödinger -Kdv Systemmentioning

confidence: 98%

“…Solitons in such a Zakharov system (ZS) were studied for the following cases: (i) for equal nonlinearity and dispersion coefficients of the LF wave (𝛽 and 𝛾, respectively, see Sec. 2 below) (𝛾/𝛽 = 1), a two-component Davydov-Scott (DS) soliton was found [18,19]; oscillations of the HF component in which were investigated in [20]; (ii) for 𝛾/𝛽 ≠ 1, an asymptotic solution in the form of a multihump soliton, assuming a sufficiently small HF field amplitude in comparison to the LF one, was found in [14]; (iii) a localized steady state of the HF wave field was found, neglecting strictional action of the HF field on LF waves, given that there exists a LF solution in the form of a "depression" soliton [17]; (iv) new two-component solitons with two free parameters were found analytically in [21] in the asymptotic approximation for an arbitrary ratio of nonlinearity 𝛽 and dispersion 𝛾; and, finally, a one-parameter family of exact two-component solitons under the condition of relatively weak dispersion, 𝛾 < 3𝛽, was found in [21].…”

Section: Introductionmentioning

confidence: 99%

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Soliton oscillations in the Zakharov-type system at arbitrary nonlinearity-dispersion ratio

Blyakhman

Gromov

Malomed

et al. 2018

Chaos, Solitons & Fractals

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The dynamics of two-component solitons with a small spatial displacement of the highfrequency (HF) component relative to the low-frequency (LF) one is investigated in the framework of the Zakharov-type system. In this system, the evolution of the HF field is governed by a linear Schrödinger equation with the potential generated by the LF field, while the LF field is governed by a Korteweg-de Vries (KdV) equation with an arbitrary dispersion-nonlinearity ratio and a quadratic term accounting for the HF feedback on the LF field. The oscillation frequency of the soliton's HF component relative to the LF one is found analytically. It is shown that the solitons are stable against small perturbations. The analytical results are confirmed by numerical simulations. Highlights:>The dynamics of the two-component (HF-LF) soliton with initial displacement of the HF component is investigated.>The study is performed in the framework of the Zakharov-type system of coupled linear-Schrödinger and KdV equations, with an arbitrary ratio of nonlinearity and dispersion coefficients. >Analytical and numerical results are produced. > The oscillation frequency of the displaced HF component of the two-component soliton is found. > Stability of the perturbed twocomponent solitons is demonstrated>.

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Section: Oscillations Of a Perturbed Solitonsupporting

confidence: 83%

Section: The Coupled Linear-schrödinger -Kdv Systemmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Soliton oscillations in the Zakharov-type system at arbitrary nonlinearity-dispersion ratio

Blyakhman

Gromov

Malomed

et al. 2018

Chaos, Solitons & Fractals

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On the quantum dynamics of Davydov solitons in proteinα-helices

Georgiev

Glazebrook

2019

Physica A: Statistical Mechanics and its Applications

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The transport of energy inside protein α-helices is studied by deriving a system of quantum equations of motion from the Davydov Hamiltonian with the use of the Schrödinger equation and the generalized Ehrenfest theorem. Numerically solving the system of quantum equations of motion for different initial distributions of the amide I energy over the peptide groups confirmed the generation of both moving or stationary Davydov solitons. In this simulation the soliton generation, propagation, and stability were found to be dependent on the symmetry of the exciton-phonon interaction Hamiltonian and the initial site of application of the exciton energy.

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Dynamics of the Davydov–Scott soliton with location or velocity mismatch of its high-frequency component

Cited by 2 publications

References 17 publications

Soliton oscillations in the Zakharov-type system at arbitrary nonlinearity-dispersion ratio

Soliton oscillations in the Zakharov-type system at arbitrary nonlinearity-dispersion ratio

On the quantum dynamics of Davydov solitons in proteinα-helices

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