Discrete modulational instability and bright localized spin wave modes in easy-axis weak ferromagnetic spin chains involving the next-nearest-neighbor coupling*

Xie, Jiayu; Deng, Zhi-Hao; Xu, Chunju; Tang, Bing

doi:10.1088/1674-1056/28/7/077501

Cited by 21 publications

(7 citation statements)

References 69 publications

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“…In the literature, many powerful techniques have been used to solve such an equation, and several types of solutions have been constructed. [41][42][43][44][45][46][47][48][49][50] Here, with the aid of the direct method, our attention is focused on the derivation of the solitary wave solutions of this equation. The kind of these solutions strongly depends on the sign of the product PQ as discussed below.…”

Section: Exact and Approximate Modulated Solitarymentioning

confidence: 99%

Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

et al. 2023

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In this paper, the control of dissipation and amplification of solitary waves in an electrical model of microtubule is demonstrated. This model is consisted of a shunt nonlinear resistance-capacitance ($J(V)-C(V)$) circuit and a series resistance-inductance $(R-L$) circuit. Through the linear dispersion analysis, two characters of the network are found, that is low band pass and bandpass characters. The effects of the conductance's parameter $\lambda$ on the linear dispersion curve are also analyzed. It appears that the increase of $\lambda$ induces a decrease (an increase) of the width of the bandpass filter for positive (negative) values of $\lambda$. By applying the reductive perturbation method, we derive the equation governing the dynamics of the modulated waves in the system. This obtained equation is the well-known nonlinear Schrödinger equation extended by a linear term proportional to an hybrid parameter $\sigma$, i.e. dissipation or amplification coefficient. Based on this parameter, we successfully demonstrate the hybrid behavior (dissipation and amplification) of the system. The exact and approximate solitary wave solutions of the obtained equation are derived and the effects of the coefficient $\sigma$ on the characteristic parameters of these waves are investigated. Using the found analytical solutions, we show numerically that the waves that are propagated throughout the system can be dissipated, amplified, or remained stable depending on the network parameters. These results are not only in agreement with the analytical predictions, but also with the existing experimental results in the literature.

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Section: Exact and Approximate Modulated Solitarymentioning

confidence: 99%

Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

et al. 2023

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“…Indeed, a wide class of discrete models have been used to highlight the nonlinear excitation modes and their applications through the MI analysis. Xie et al [7], have exhibited the formation of discrete MI growth rates and localized bright soliton in weak ferromagnetic spin chains. They have used the effects of the next-nearest neighbor to display the unstable modes and stable zones.…”

Section: Introductionmentioning

confidence: 99%

“…In [11], the authors have depicted the chaos-like motion and unstable modes incited by the self-modulated Kerr nonlinearity in optomechanical arrays. The discrete nonlinear Schrödinger equation (DNLSE) is the most well-known discrete model during MI analysis, and localized modes [1][2][3][4][5][6][7][8][9][10][11]. For example, in [25] the authors used the discrete cubic-quintic NLSE to show the effects of the nonlinear terms on the train of waves propagating in the forbidden gap (FG).…”

Section: Introductionmentioning

confidence: 99%

Discrete modulation instability and localized waves of the coupled semi-discrete Hirota equation

Houwe

Abbagari

Akinyemi

et al. 2023

Preprint

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In this paper, we use the numerical simulation of the discrete Hirota equation to point out the localized modes and wave patterns. The discrete modulation instability is used to demonstrate how the nonlinear term generates unstable or stable modes when a little perturbation is introduced. We have also stated that for strong enough nonlinear terms, new bands emerge. Furthermore, by applying an external periodic force, we were able to push one end of the discrete Hirota model into the forbidden frequency gap. We established the threshold amplitude expression and the driven amplitude. According to one finding, the threshold of supratransmission decreases as the nonlinear term of the discrete Hirota equation increases. For specific times of propagation, we showed the propagation of the train of waves as well as the modulated wave patterns. We demonstrated the wave train traveling through the band gap, where energy jumps from the bottom to the top and vice versa, over a significant period of time. These findings will almost certainly pave the way for new nonlinear dynamics applications.

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“…Finally results from studies carried out, strongly suggests that the NNN coupling accounts for interesting phenomena in discrete lattices. These include the identification of the staggering and unstaggering stationary localized breather modes [20], observation of pulse propagation in nonlinear photonic crystal wave guides [36], existence of bright and dark discrete breathers in 4 nonlinear lattice [37], linear increase of the input power required for soliton formation in lattices [38], and the reversal phenomenon of the propagation direction of the Brillouin zone boundary mode [39]. This study mainly captures a generic model of an atomic lattice and theoretically investigate on the effects of the NNN coupling, with potential applications in quantum-information storage [40] and DNA systems [41] serving like a driving force behind our current investigation.…”

Section: Introductionmentioning

confidence: 99%

Modulational Instability and Discrete Localized Modes in Two Coupled Atomic Chains with Next-Nearest-Neighbor Interactions

Nfor

Yamgoué

2022

J Nonlinear Math Phys

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A pair of one dimensional atomic chains which are coupled via the Klein-Gordon potential is considered in this study, with each chain experiencing both nearest and next-nearest-neighbor interactions. The discrete nonlinear Schrödinger amplitude equation with next-nearest-neighbor interactions is thus derived from the out-phase equation of motion of the coupled chains. This is achieved by using the rotating wave approximations perturbation method, in which both the carrier wave and envelope are explicitly treated in the discrete regime. It is shown that the next-nearest-neighbor interactions greatly modifies the region of observation of modulational instability in the atomic chain. By exploring the discrete Hirota-Bilinear method, we obtain the discrete one-soliton solution which is localized around the origin and structurally stable because it conserves it form as time evolves. However when the atomic chain is purely subjected to a symmetric coupling potential, we observe a structurally unstable discrete excitation that changes into an up-and-down asymmetric localized modes; both in the presence and absence of next-nearest-neighbor interactions. Results of numerical simulations clearly depicts the long term evolution of these discrete nonlinear excitations, that evolve from symmetric to asymmetric localized modes in the atomic chain.

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Discrete modulational instability and bright localized spin wave modes in easy-axis weak ferromagnetic spin chains involving the next-nearest-neighbor coupling*

Cited by 21 publications

References 69 publications

Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

Discrete modulation instability and localized waves of the coupled semi-discrete Hirota equation

Modulational Instability and Discrete Localized Modes in Two Coupled Atomic Chains with Next-Nearest-Neighbor Interactions

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