Synergetics of Molecular Systems

Lupichev, L. N.; Savin, A. V.; Kadantsev, Vasiliy N.

doi:10.1007/978-3-319-08195-3

Cited by 12 publications

(26 citation statements)

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“…The dynamic analysis of the interaction process of solitons is a very important topic in studies of nonlinear waves [7,26,32,67]. In the process of collision, the multiple-solitons may be excited.…”

Section: A Dynamic Analysis Of Soliton Solutionsmentioning

confidence: 99%

“…As is well known, a soliton is a solitary wave that can propagate stably with the dynamic behavior like a "particle." A solitary wave was shown to be an ideal method for transferring vibrational excitations [26]. Indeed, the discovery of phononic solitons has been demonstrated to be of fundamental importance in the study of nonlinear phenomena in phononic crystals.…”

Section: Introductionmentioning

confidence: 99%

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Solitary waves in a granular chain of elastic spheres: Multiple solitary solutions and their stabilities

2019

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A granular chain of elastic spheres via Hertzian contact incorporates a classical nonlinear force model describing dynamical elastic solitary wave propagation. In this paper, the multiple solitary waves and their dynamic behaviors and stability in such a system are considered. An approximate KdV equation with the standard form is derived under the long-wavelength approximation and small deformation. The closed-form analytical single-and multiple-soliton solutions are obtained. The construction of the multiple-soliton solutions is analyzed by using the functional analysis. It is found that the multiple-soliton solution can be excited by the single-soliton solutions. This result is confirmed by the numerical analysis. Based on the soliton solutions of the KdV equation, the analytic solutions of multiple dark solitary waves are obtained from the original dynamic equation of the granular chain in the long-wavelength approximation. The stability of the single and multiple dark solitary wave solutions are numerically analyzed by using both split-step Fourier transform method and Runge-Kutta method. The results show that the single dark solitary wave solution is stable, and the multiple dark solitary waves are unstable.

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Section: A Dynamic Analysis Of Soliton Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solitary waves in a granular chain of elastic spheres: Multiple solitary solutions and their stabilities

2019

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“…In the present paper, we further developed the quantum dynamic model of the collective excitations in α-helical protein structures (Davydov, 1977), (Kadantsev, Lupichov and Savin, 1987;Lupichev, Savin and Kadantsev, 2015), (Takeno, 1984) and extended this approach to taking into account the dynamics of the side-chains of residues responsible for the protein interaction within the environment. In the model, we considered a side-chain-dependent et al, 1986;Bolterauer and Tuszyński, 1989;Bolterauer, Tuszyński and Satarić, 1991;Mesquita, Vasconcellos and Luzzi, 2004).…”

Section: Discussion: Vibrational Modes and Self-organization In α-Helmentioning

confidence: 99%

“…Dispersion curves for the chain of hydrogen-bounded PGs calculated at the following elastic constants(Lupichev, Savin and Kadantsev, 2015). (a) s=1, χ 1,2 = 13.0 N −1 , χ 2,1 = 17.0 N −1 , χ 0,1 = 5.0 N −1 , χ 0,2 = 0 N −1 .…”

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confidence: 99%

Collective Excitations in α-helical Protein Structures Interacting with the Water Environment

Kadantsev

Goltsov

2018

Preprint

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Low-frequency vibrational excitations of protein macromolecules in the terahertz frequency region are suggested to contribute to many biological processes such as enzymatic activity, energy/charge transport, protein folding, and others. To explain high effectiveness of energy storage and transport in proteins, two possible mechanisms of the long-lived excitation in proteins were proposed by H. Fröhlich and A.S. Davydov in the form of either vibrational modes or solitary waves, respectively. In this paper, we developed a quantum dynamic model of vibrational excitation in α-helical proteins interacting with their environment formed by water molecules. In the model, we distinguished three coupled subsystems, i.e. (i) a chain of hydrogen-bonded peptide groups (PGs), interacting with (ii) the subsystem of side residuals which in turn interacts with (iii) the environment, surrounding water responsible for dissipation and fluctuation processes in the system. It was shown that under reasonable approximations the equation of motion for phonon variables of the PG chain can be transformed to nonlinear Schrodinger equation for order parameter which admits bifurcation into the solution corresponding to weak damped vibrational modes (Fröhlich-type regime). A bifurcation parameter in the model is derived through the strength of interaction between alpha-helical protein and its environment. As shown, in the bifurcation region, a solution corresponding to Davydov soliton can exist. The suggested mechanism underlying emerging macroscopic dissipative structures in the form of collective vibrational modes is discussed in connection with the recent experimental data on the long-lived collective protein excitations in the terahertz frequency region.

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“…A solitary wave was shown to be an ideal method for transferring vibrational excitations [5]. Elastic spherical chain is an ideal experimental device for studying nonlinear science.…”

Section: Introductionmentioning

confidence: 99%

The Exact Solitary Wave Solutions in Continuity Equation of the One-Dimensional Granular Crystals of Elastic Spheres

Liu¹,

Zhang²

2019

JAMP

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In this paper, we reduced the governing equation describing the one-dimensional granular crystals of elastic spheres to a continuous equation by small deformation and long wave approximation. Then, the G'/G-expansion method is applied to this continuous equation, and the exact solitary wave solutions with arbitrary parameters are obtained. Compared with other papers, the solutions obtained in this paper are more extensive and contains more parameters. The simultaneous existence of exact solitary wave solutions can help us study the propagation of shock waves in one-dimensional granular crystals of elastic spheres. At the same time, it has important theoretical significance in nondestructive testing with non-linear wave.

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Synergetics of Molecular Systems

Cited by 12 publications

References 0 publications

Solitary waves in a granular chain of elastic spheres: Multiple solitary solutions and their stabilities

Solitary waves in a granular chain of elastic spheres: Multiple solitary solutions and their stabilities

Collective Excitations in α-helical Protein Structures Interacting with the Water Environment

The Exact Solitary Wave Solutions in Continuity Equation of the One-Dimensional Granular Crystals of Elastic Spheres

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