Traveling waves and bifurcations for the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation

Yang, Deniu

doi:10.1016/j.ijleo.2021.168058

Cited by 16 publications

(4 citation statements)

References 22 publications

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“…where 𝜔 𝑗 and ω𝑗 are column and row vectors. Taking the Hermitian to (22) and utilizing (21), we see that…”

Section: Soliton Solutionsmentioning

confidence: 99%

On multi-soliton solutions to the Heisenberg ferromagnetic spin chain equation in (2+1)-dimensions

Kang¹,

Yang²

2022

Preprint

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This paper concentrates on the Heisenberg ferromagnetic spin chain (HFSC) equation in (2+1)-dimensions modelling nonlinear wave propagation in ferromagnetic spin chain. A variable transformation is first employed to reduce the studied equation. And then an associated matrix Riemann-Hilbert problem is built on the real line through analyzing spectral problem of the reduced equation. As a consequence, solving the obtained matrix Riemann-Hilbert problem with the identity jump matrix, corresponding to the reflectionless, the general multi-soliton solutions to the HFSC equation in (2+1)-dimensions are acquired. Specially, the one-and two-soliton solutions are worked out and analyzed graphically.

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“…where 𝜔 𝑗 and ω𝑗 are column and row vectors. Taking the Hermitian to (22) and utilizing (21), we see that…”

Section: Soliton Solutionsmentioning

confidence: 99%

On multi-soliton solutions to the Heisenberg ferromagnetic spin chain equation in (2+1)-dimensions

Kang¹,

Yang²

2022

Preprint

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“…By using the "three-step method" of Professor Li's method together with the phase orbit of system (8) [13][14][15][16][17], the traveling wave solution of (1) can be constructed.…”

Section: Traveling Wave Solutions Of (1)mentioning

confidence: 99%

Phase Portraits and Bounded and Singular Traveling Wave Solution of Stochastic Nonlinear Biswas–Arshed Equation

Tang

Zeng

2022

Discrete Dynamics in Nature and Society

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The main purpose of the current paper is to study the phase portraits and bounded and singular traveling wave solution of the stochastic nonlinear Biswas–Arshed equation by using the “three-step method” of Professor Li’s method together with the phase orbit of planar dynamical system. Firstly, by employing the traveling wave transformation, the stochastic nonlinear Biswas–Arshed equation is simplified into deterministic nonlinear ordinary differential equation. Secondly, phase portraits of the stochastic nonlinear Biswas–Arshed equation are plotted by analyzing the planar dynamic system of the nonlinear ordinary differential equation. Finally, the bounded and singular traveling wave solutions of the stochastic nonlinear Biswas–Arshed equation are constructed.

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“…In [34], the Jacobi elliptic expansion method is adopted and bright and dark soliton solutions are obtained. In [35], the theory of dynamical systems is introduced for constructing the bounded traveling wave solutions. In [36], the modified Khater method is carried out to deal with Eq.…”

Section: Introductionmentioning

confidence: 99%

Abundant Soliton Structures to the ( $2 + 1$ )-Dimensional Heisenberg Ferromagnetic Spin Chain Dynamical Model

Wang

Shi

Wang

2023

Advances in Mathematical Physics

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In this paper, we aim to investigate the ( 2 + 1 )-dimensional Heisenberg ferromagnetic spin chain equation that is used to describe the nonlinear dynamics of magnets. Two recent effective technologies, namely, the variational method and subequation method, are employed to construct the abundant soliton solutions. By these two methods, diverse solutions such as the bright soliton, dark soliton, bright-dark soliton, perfect periodic soliton, and singular periodic soliton are successfully extracted. The numerical results are illustrated in the form of 3-D plots and 2-D curves by choosing proper parametric values to interpret the dynamics of wave profiles. Finally, the physical interpretation of the acquired results is elaborated in detail. The results obtained in this study are helpful to explain some physical meanings of some nonlinear physical models in electromagnetic waves.

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Traveling waves and bifurcations for the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation

Cited by 16 publications

References 22 publications

On multi-soliton solutions to the Heisenberg ferromagnetic spin chain equation in (2+1)-dimensions

On multi-soliton solutions to the Heisenberg ferromagnetic spin chain equation in (2+1)-dimensions

Phase Portraits and Bounded and Singular Traveling Wave Solution of Stochastic Nonlinear Biswas–Arshed Equation

Abundant Soliton Structures to the ( $2 + 1$ )-Dimensional Heisenberg Ferromagnetic Spin Chain Dynamical Model

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Traveling waves and bifurcations for the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation

Cited by 16 publications

References 22 publications

On multi-soliton solutions to the Heisenberg ferromagnetic spin chain equation in (2+1)-dimensions

On multi-soliton solutions to the Heisenberg ferromagnetic spin chain equation in (2+1)-dimensions

Phase Portraits and Bounded and Singular Traveling Wave Solution of Stochastic Nonlinear Biswas–Arshed Equation

Abundant Soliton Structures to the ( 2 + 1 )-Dimensional Heisenberg Ferromagnetic Spin Chain Dynamical Model

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Abundant Soliton Structures to the ( $2 + 1$ )-Dimensional Heisenberg Ferromagnetic Spin Chain Dynamical Model