Modulational instability, quantum breathers and two-breathers in a frustrated ferromagnetic spin lattice under an external magnetic field

Su, Wanhan; Xie, Jiayu; Wu, Tianle; Tang, Bing

doi:10.1088/1674-1056/27/9/097501

Cited by 11 publications

(2 citation statements)

References 78 publications

(93 reference statements)

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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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“…[9] Theoretically, a particular region of wave numbers of the plane wave configurations becomes unstable to modulations due to the modulational instability, which leads to the rapid growth of the unstable modes and eventually to localization in configuration space. In nonlinear systems, the modulational instability is of crucial significance for creating localized excitations, such as bright solitons, [10][11][12][13] breathers, [14,15] and rogue waves. [16] In general, the modulational instability is a vital characteristic of continuum and discrete nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

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

Xie

Deng

et al. 2019

Chinese Phys. B

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We report a theoretical work on the properties of modulational instability and bright type nonlinear localized modes in one-dimensional easy-axis weak ferromagnetic spin lattices involving next-nearest-neighbor couplings. With a linear stability analysis, we calculate the growth rates of the modulational instability, and plot the instability regions. When the strength of the next-nearest-neighbor coupling is large enough, two new asymmetric modulational instability regions appear near the boundary of the first Brillouin zone. Furthermore, analytical forms of the bright nonlinear localized modes are constructed by means of a quasi-discreteness approach. The influence of the next-nearest-neighbor coupling on the Brillouin zone center mode and boundary mode are discussed. In particular, we discover a reversal phenomenon of the propagation direction of the Brillouin zone boundary mode.

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Characteristics and interactions of solitary and lump waves of a (2 + 1)-dimensional coupled nonlinear partial differential equation

Ren

2019

Nonlinear Dyn

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Modulational instability, quantum breathers and two-breathers in a frustrated ferromagnetic spin lattice under an external magnetic field

Cited by 11 publications

References 78 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 modulational instability and bright localized spin wave modes in easy-axis weak ferromagnetic spin chains involving the next-nearest-neighbor coupling*

Characteristics and interactions of solitary and lump waves of a (2 + 1)-dimensional coupled nonlinear partial differential equation

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