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

Osman, M. S.; Tariq, Kalim U.; Bekir, Ahmet; Elmoasry, Ahmed; Elazab, Nasser S.; Younis, Muhammad; Abdel‐Aty, Mahmoud

doi:10.1088/1572-9494/ab6181

Cited by 106 publications

(21 citation statements)

References 40 publications

(43 reference statements)

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“…for α 2 (α 3 + α 5 ) > 0. To find the solution of Equation (1.1), let us consider the U(ξ ) = a 0 + m i=1 (a i Z i + b i Z −i ) form of the solution (see also [18]), where Z ′ = γ + Z 2 , a ′ i s, b ′ i s, and γ are the real parameters. The parameters are to be determined later.…”

Section: Analytical Analysismentioning

confidence: 99%

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Investigation of Electromagnetic Wave Structures for a Coupled Model in Anti-ferromagnetic Spin Ladder Medium

et al. 2020

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The article studies the extraction of electromagnetic wave structures in a spin ladder anti-ferromagnetic medium with a coupled generalized non-linear Schrodinger model. The direct algebraic technique is used to extract the wave solutions. The solutions are obtained in the form of dark, singular, kink, and dark-singular under different constraint conditions. Moreover, the dynamic behavior of the structures have depicted in 3D graphs and their corresponding counterplots. The results are helpful for the understanding of wave propagation study and are also vital for numerical and experimental verifications in the field of electromagnetic wave theory.

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Section: Analytical Analysismentioning

confidence: 99%

“…It arises by balancing dispersive and non-linear terms. Solitons are discussed in different fields, and for references see [10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Investigation of Electromagnetic Wave Structures for a Coupled Model in Anti-ferromagnetic Spin Ladder Medium

et al. 2020

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“…Some conditions of integrability were given which guarantee the existence of solitons (Tang et al 2017). In Osman et al (2020), constructio0n of further exact soliton solutions of the (2 + 1)-dimensional HFSCE and investigating the nonlinear dynamics of magnets and explains their ordering in ferromagnetic materials were carried.. The collision dynamics of soliton in discrete classical ferromagnetic spin chain with Dzyaloshinskii-Moriya (DM) interaction in the classical limit are analyzed (Parasuraman 2019).…”

Section: Introductionmentioning

confidence: 99%

Longitudinal-transverse soliton chains analog to heisenberg ferromagnetic spin chains in (2+1) dimensional with biquadrant interactions

Abdel‐Gawad

2022

Opt Quant Electron

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In quantum spin systems, lower energy state for a nuclear spin in an external field is spin ($$+1/2$$ + 1 / 2 ) while the higher energy state is spin ($$-1/2$$ - 1 / 2 ). A continuum analog to the discrete model led to nonlinear Schrodinger equation (NLSE) with higher order dispersion. Recently, a model equation with bilinear and biquadratic interactions in the (2 + 1) dimensional Heisenberg ferromagnetic spin chain (HFSC), was derived in the literature. This model equation is a NLSE with quartic dispersion and fifth degree nonlinearity, and it was rarely considered in the literature. The, only, work done has shown solitons solutions. This motivated us to consider this problem for inspecting the multiple characteristics of the HFSC in space-time. Here, the exact solutions of the HFSC biquadratic model equation are obtained by using the unified method (UM). In applications, it is found the UM is of low time cost in symbolic computations. So, we think that it prevails the known methods. The solutions obtained are evaluated numerically and shown in figures.These figures reveal that the solutions exhibit longitudinal-transverse (L-T) solitons chains (SCs) with presence (or absence) of tunneling, depending on the values of the parameters of high dispersivity and high nonlinearity. Also, L-T zig-zag SCs are observed, where pulses with higher amplitudes (or gaps) occur along a characteristic line. Furthermore, L-TSCs modulation along the space axes is shown. It is remarked that the contour plots show complex lattice waves, which is relevant to the spin chain system. So, the present work reveals new solitons structures induced by bilinear-biquadratic interactions of HFSC.

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“…An ansatz method,to solve The HFSC equation was used to get bright and dark 1-soliton solutions.Some conditions of integrability were given which guarantee the existence of solitons [18]. In [19], constructio0n of further exact soliton solutions of the (2 + 1)-dimensional HFSCE and investigating the nonlinear dynamics of magnets and explains their ordering in ferromagnetic materials were carried.. The collision dynamics of soliton in discrete classical ferromagnetic spin chain with Dzyaloshinskii-Moriya (DM) interaction in the classical limit are analyzed [20].…”

Section: Introductionmentioning

confidence: 99%

Continuum Soliton Chain Analog to Heisenberg Spin Chain System. Modulation Stability and Spectral Characteristics

Abdel‐Gawad

2022

Int J Theor Phys

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The one-dimensional (1D) Heisenberg spin chain system (HSCS) allows to investigate anomalous features originating from strong quantum fluctuations, which become more significant than those in higher dimensions. A continuum model equation of the HSCS, based on the discrete model, was constructed in the literature. It is nonlinear Schrodinger equation (NLSE) with biquadratic dispersion and fifth degree nonlinearity. Rare research works were done in this area. Notably for deriving the exact solutions and investigate the physical phenomena produced. Our objective, here, is to obtain these solutions, which we think they are new. Further, an analog of the different geometric solutions structures to the known characteristics of HSCS is performed. The unified method is implemented to find the exact solutions of the continuum model equation. A variety of solutions are obtained where they are evaluated numerically and represented in graphs. In these graphs, it is remarked that the solutions exhibit soliton chain (or dense soliton chain).in an analog to spin chain. In the contour plots, they show different shapes of super lattices. Furthermore, complex chirped waves are observed. A significant result is that these solutions are bounded by −1/4 and 1/4, which can be relevant to the spins−1/2 and 1/2. The analysis of modulation stability is carried and it is found that there is a critical value for the dominant parameters, where below this value, modulation instability holds otherwise modulation stability occurs.For the spectral characteristics, it is shown that the wave number increases abruptly and decreases to an asymptotic state, while the frequency is monotonic increasing. The spectrum is periodic wave away from the origin, but near the origin it is soliton.

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

Cited by 106 publications

References 40 publications

Investigation of Electromagnetic Wave Structures for a Coupled Model in Anti-ferromagnetic Spin Ladder Medium

Investigation of Electromagnetic Wave Structures for a Coupled Model in Anti-ferromagnetic Spin Ladder Medium

Longitudinal-transverse soliton chains analog to heisenberg ferromagnetic spin chains in (2+1) dimensional with biquadrant interactions

Continuum Soliton Chain Analog to Heisenberg Spin Chain System. Modulation Stability and Spectral Characteristics

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