Nonlinear excitations in a disordered alpha-helical protein chain

Veni, S. Saravana; Latha, M.M.

doi:10.1016/j.physa.2014.03.087

Cited by 14 publications

(5 citation statements)

References 25 publications

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“…show that the strong-interactions of third-order RWs nearly agree with the exact solution (18). If a small noise adds to the exact solution (18) in strong-interaction case, the wave propagation behaves well except a small bulge around the edges(see Fig. 7(c)).…”

Section: ) and 2(e))mentioning

confidence: 58%

“…(1) has been constructed [15] by using Hirota method. Multisoliton solutions using Darboux transformation is presented in [18]. Besides, Eq.…”

Section: Introductionmentioning

confidence: 99%

“…Figure7: The third-order RW solutions(18). The exact solution (a) d 1,2 = f 1,2 = 0 and (d) d 1 = 10, d 2 = f 1,2 = 0 (left); (b) and (e) simulated simulation using exact solutions(18) as the initial conditions (middle); (c) and (f) numerical simulations by adding random noise with amplitude 2% to the exact solutions(18) as initial conditions (right).…”

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confidence: 99%

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Multi-rogue wave solutions for a generalized integrable discrete nonlinear Schrödinger equation with higher-order excitations

Yang

Zhang

2021

Nonlinear Dyn

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In this paper, we construct the discrete rogue wave(RW) solutions for a higher-order or generalized integrable discrete nonlinear Schrödinger(NLS) equation. First, based on the modified Lax pair, the discrete version of generalized Darboux transformation are constructed. Second, the dynamical behaviors of first-, second-and third-order RW solutions are investigated in corresponding to the unique spectral parameter λ, higher-order term coefficient γ, and free constants d k , f k (k = 1, 2, • • • , N ), which exhibit affluent wave structures. The differences between the RW solution of the higher-order discrete NLS equation and that of the Ablowitz-Ladik(AL) equation are illustrated in figures. Moreover, numerical experiments are explored, which demonstrates that strong-interaction RWs are stabler than the weak-interaction RWs. Finally, the modulation instability of continuous waves is studied.

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Section: ) and 2(e))mentioning

confidence: 58%

“…(1) has been constructed [15] by using Hirota method. Multisoliton solutions using Darboux transformation is presented in [18]. Besides, Eq.…”

Section: Introductionmentioning

confidence: 99%

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Multi-rogue wave solutions for a generalized integrable discrete nonlinear Schrödinger equation with higher-order excitations

Yang

Zhang

2021

Nonlinear Dyn

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“…For some time past, the investigations of physical properties of proteins (particularly, such as transfer of energy or transfer of charge [1]) are performed taking into account their actual structure [2–10] with increasing frequency. In effect, amino acid inhomogeneity [2, 3], discreteness [4, 5], finite length of the α-spiral section [6], and other factors [7–10] are inherent in general to the structures containing carbon [11–13].…”

Section: Introductionmentioning

confidence: 99%

“…In effect, amino acid inhomogeneity [2, 3], discreteness [4, 5], finite length of the α-spiral section [6], and other factors [7–10] are inherent in general to the structures containing carbon [11–13]. Particularly, average-electron structure and average-nuclear structure of the protein molecule were analysed in detail in article [14].…”

Section: Introductionmentioning

confidence: 99%

Current in the Protein Nanowires: Quantum Calculations of the Base States

Suprun¹,

Shmeleva²

2016

Nanoscale Res Lett

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It is known that synthesis of adenosine triphosphoric acid in mitochondrions may be only completed on the condition of transport of the electron pairs, which were created due to oxidation processes, to mitochondrions. As of today, many efforts were already taken in order to understand those processes that occur in the course of donor-acceptor electron transport between cellular organelles (that is, between various proteins and protein structures). However, the problem concerning the mechanisms of electron transport over these organelles still remains understudied. This paper is dedicated to the investigation of these same issues.It has been shown that regardless of the amino acid inhomogeneity of the primary structure, it is possible to apply a representation of the second quantization in respect of the protein molecule (hereinafter “numbers of filling representation”). Based on this representation, it has been established that the primary structure of the protein molecule is actually a semiconductor nanowire. In addition, at the same time, its conduction band, into which an electron is injected as the result of donor-acceptor processes, consists of five sub-bands. Three of these sub-bands have normal dispersion laws, while the rest two sub-bands have abnormal dispersion laws (reverse laws). Test calculation of the current density was made under the conditions of the complete absence of the factors, which may be interpreted as external fields. It has been shown that under such conditions, current density is exactly equal to zero. This is the evidence of correctness of the predictive model of the conductivity band of the primary structure of the protein molecule (protein nanowire). At the same time, it makes it possible to apply the obtained results in respect of the actual situation, where factors, which may be interpreted as external fields, exist.

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Continuum limits for rational, breather solutions, and gauge equivalent model of the generalized discrete nonlinear Schrödinger equation

Huang

Zhang

et al. 2023

Math Methods in App Sciences

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In this paper, we focus on an integrable higher‐order discrete nonlinear Schrödinger (dNLS) equation, which yields the Lakshmanan–Porsezian–Daniel (LPD) equation in the continuum limit. The breather solutions of the higher‐order dNLS are obtained for the first time. We show that the rational solutions and breather solutions of the higher‐order dNLS equation yield the counterparts of the integrable fourth‐order NLS equation under proper continuous limits. Most importantly, we also explore the gauge equivalent equation of the higher‐order dNLS equation from the point of view of the continuous limit theory. We make integrable discretization for the linear spectrum problem of the integrable generalized Heisenberg ferromagnetic equation that is just the gauge equivalent structure of the LPD equation. Compatibility condition of the discrete linear spectrum problem leads to a discrete integrable generalized Heisenberg Ferromagnetic equation. It is revealed that the discrete linear spectrum problem of the discrete integrable generalized ferromagnetic equation converges to the corresponding spectrum problem of the integrable generalized Feisenberg spin model in the continuum limit.In addition, with the help of the method of linear combinations for the conserved fluxes and densities, the conservation laws of the integrable higher‐order dNLS equation converge to the homologous results of the LPD equation.

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Nonlinear excitations in a disordered alpha-helical protein chain

Cited by 14 publications

References 25 publications

Multi-rogue wave solutions for a generalized integrable discrete nonlinear Schrödinger equation with higher-order excitations

Multi-rogue wave solutions for a generalized integrable discrete nonlinear Schrödinger equation with higher-order excitations

Current in the Protein Nanowires: Quantum Calculations of the Base States

Continuum limits for rational, breather solutions, and gauge equivalent model of the generalized discrete nonlinear Schrödinger equation

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