Analytic study on a (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si30.gif" display="inline" overflow="scroll"><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>)-dimensional nonlinear Schrödinger equation in the Heisenberg ferromagnetism

Liu, De-Yin; Tian, Bo; Jiang, Yan; Xie, Xin; Wu, Xiao-Yu

doi:10.1016/j.camwa.2016.03.020

Cited by 45 publications

(12 citation statements)

References 20 publications

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“…and elliptic NLS equation otherwise. 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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“…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.

107

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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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“…The nonlinear spin excitations in the HFSC are of great significance to the application of spintronic components and magnetic devices, such as magnetic field sensors and high-density data storage [39,40]. Different types of NLS equations and their soliton solutions have been proposed to study the nonlinear dynamics of the HFSC system [38,[41][42][43][44]. Dark soliton interactions in an inhomogeneous one-dimensional HFSC system, which is modelled by a fourth-order variable-coefficient NLS equation, have been investigated [45].…”

Section: Introductionmentioning

confidence: 99%

Transformation of soliton states for a (2+1) dimensional fourth-order nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain

et al. 2019

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In this paper, we investigate the soliton interaction in the Heisenberg ferromagnetic spin chain (HFSC), which is governed by a (2+1) dimensional fourth-order nonlinear Schrödinger equation. Research on the transformation of soliton states in the HFSC plays a significant role in the applications of magnetic devices and spintronic components. The soliton solutions are obtained by the Hirota bilinear method. Bound state solitons and different transmission states of periodic discrete wave packets formed by soliton interactions are depicted. Besides, a new phenomenon, that two solitons bound together originally are completely separated after three solitons interact with each other, is presented. The effects of corresponding parameters on the soliton propagation and interaction are discussed. The methods to control the amplitude, duration, intensity and phase of solitons are described. The obtained results may be useful to study the nonlinear characteristics of magnetic materials.

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Analytic study on a (2+1)-dimensional nonlinear Schrödinger equation in the Heisenberg ferromagnetism

Cited by 45 publications

References 20 publications

Hybrid behavior of a two-dimensional Noguchi nonlinear electrical network

Hybrid behavior of a two-dimensional Noguchi nonlinear electrical network

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

Transformation of soliton states for a (2+1) dimensional fourth-order nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain

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