Dark solitonic interaction and conservation laws for a higher-order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si85.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional nonlinear Schrödinger-type equation in a Heisenberg ferromagnetic spin chain with bilinear and biquadratic interaction

Wang, Qimin; Gao, Yi–Tian; Su, Chuan-Qi; Mao, Bing-Qing; Gao, Zhe; Yang, Jinwei

doi:10.1016/j.aop.2015.10.001

Cited by 36 publications

(5 citation statements)

References 38 publications

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“…Each version of this equation has been extensively studied, largely due to the fact that they describe many types of physical phenomena, including rogue waves in the Heisenberg ferromagnetic spin chain [65][66][67][68][69][70], breathers in two-dimensional Fermi-Pasta-Ulam lattice [56], electromagnetic pulse propagation in optical waveguides [71], cyclotron waves in plasmas [72] and surface waves in deep water [73]. It is also important to note that several special or general cases of equation (8) occur in various fields of applied physics [74][75][76][77][78][79][80].…”

Section: Amplitude Equationmentioning

confidence: 99%

Hybrid behavior of a two-dimensional Noguchi nonlinear electrical network

2021

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In this work, the propagation of modulated waves in a nonlinear two-dimensional discrete electrical line is studied. Based on the linear dispersive law, we demonstrate that the network can adopt Hybrid’s behavior due to the fact that, without changing its appearance structure or its parameters values, it can become alternatively, a purely right-handed line, a purely left-handed line or a composite right-left-handed line depending on coupling transverse parameters L 2 , C 2 and k 2 . Using the reductive perturbation method, a (2+1)-dimensional nonlinear Schrodinger equation governing the dynamics of the small amplitude signals in the network is derived and the impact of the above transverse parameters on the sign of the product of their coefficients is examined. Likewise, backward and forward solitary wave propagations in the system is predicted and analyzed quantitatively and qualitatively. The effects of relevant transverse network parameters on the characteristic parameters of these waves are investigated. We find out that these transverse parameters considerably affect the characteristics and the nature of the waves that are propagated throughout the system.

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Section: Amplitude Equationmentioning

confidence: 99%

Hybrid behavior of a two-dimensional Noguchi nonlinear electrical network

2021

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“…It plays an important role in the modern magnetic theory, which describes nonlinear magnet dynamics and is used in optical fibers. Due to the importance of DHFE, many authors have attained the exact solution for this equation by using various methods, such as Hirota's bilinear method [13,14], Darboux transformation [15][16][17], sub-ODE method [18], sine-Gordon and modified exp-function expansion methods [19], auxiliary ordinary differential equation [20], Jacobi elliptic functions [21], F-expansion method combined with Jacobi elliptic functions [22], and generalized Riccati mapping method and improved auxiliary equation [23], while many authors have investigated the analytical solutions of fractional DHFE by using various methods, including exp (−ϕ(ς))-expansion and extended tanh function [24], new extended generalized Kudryashov [25], and generalized Riccati equation mapping methods [26].…”

Section: Introductionmentioning

confidence: 99%

The solitary wave solutions of the stochastic Heisenberg ferromagnetic spin chain equation using two different analytical methods

Al-Askar

2023

Front. Phys.

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Here, we consider the stochastic (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation which is forced by the multiplicative Brownian motion in the Stratonovich sense. We utilize the (G′/G)-expansion method and the mapping method to attain the analytical solutions of the stochastic (2 + 1)-dimensional Heisenberg ferromagnetic chain equation. Various types of analytical stochastic solutions, such as the hyperbolic, elliptic, and trigonometric functions, have been obtained. Physicists can utilize these solutions to understand a variety of important physical phenomena because the magnetic soliton has been categorized as one of the interesting groups of nonlinear excitations representing spin dynamics in the semiclassical continuum Heisenberg systems. Moreover, we employ MATLAB tools to plot 3D and 2D graphs for some obtained solutions to address the influence of Brownian motion on these solutions.

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“…Solitons have been widely studied in theory and experiment in recent years. Nowadays, the investigation of the soliton solutions of a number of complex nonlinear equations plays a considerable role due to the expectant effectuation in the real world, especially in different aspects of mathematical and physical phenomena [1][2][3][4][5][6][7][8][9]. Most complex phenomena arising in applied science, such as nuclear physics, chemical reactions, signal processing, optical fibers, fluid mechanics, plasma, nonlinear optics and ecology, can be sometimes modeled and described by these equations.…”

Section: Introductionmentioning

confidence: 99%

Investigation of soliton solutions with different wave structures to the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation

Osman¹,

Tariq²,

Bekir³

et al. 2020

Commun. Theor. Phys.

106

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The principal objective of this article is to construct new and further exact soliton solutions of the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation which investigates the nonlinear dynamics of magnets and explains their ordering in ferromagnetic materials. These solutions are exerted via the new extended FAN sub-equation method. We successfully obtain dark, bright, combined bright-dark, combined dark-singular, periodic, periodic singular, and elliptic wave solutions to this equation which are interesting classes of nonlinear excitation presenting spin dynamics in classical and semi-classical continuum Heisenberg systems. 3D figures are illustrated under an appropriate selection of parameters. The applied technique is suitable to be used in gaining the exact solutions of most nonlinear partial/fractional differential equations which appear in complex phenomena.

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Dark solitonic interaction and conservation laws for a higher-order (2+1)-dimensional nonlinear Schrödinger-type equation in a Heisenberg ferromagnetic spin chain with bilinear and biquadratic interaction

Cited by 36 publications

References 38 publications

Hybrid behavior of a two-dimensional Noguchi nonlinear electrical network

Hybrid behavior of a two-dimensional Noguchi nonlinear electrical network

The solitary wave solutions of the stochastic Heisenberg ferromagnetic spin chain equation using two different analytical methods

Investigation of soliton solutions with different wave structures to the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation

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