1-Soliton solutions of the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain model with the beta time derivative

Hosseini, K.; Kaur, Lovepreet; Mirzazadeh, Mohammad; Başkonuş, Hacı Mehmet

doi:10.1007/s11082-021-02739-9

Cited by 72 publications

(17 citation statements)

References 42 publications

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“…Let us review the beta-derivative [21][22][23][24][25] as follows: Definition 1 Let ϕ : [a, ∞) → R, then the fractional beta-derivative of ϕ of order β is defined as…”

Section: Beta-fractional Derivativementioning

confidence: 99%

“…(15)(16)(17)(18)(19)(20) represents the Jacobi elliptic functions Eq. (21)(22)(23)(24)(25)(26) shows the solitonic nature comes from hyperbolic function and Eq. (27-30) are trigonometric function exhibit as periodic waves.…”

Section: Graphical Representationmentioning

confidence: 99%

“…This technique also bases on the homogeneous balance method which is an influential procedure for achieving solutions of fractional PDE introduced by Zhang and Zhang [17]. According to this method, fractional complex transform and some useful formulas of fractional beta-derivative [21][22][23][24][25] are applies to transform the nonlinear s-tfEW equation to ordinary differential equation.…”

Section: Introductionmentioning

confidence: 99%

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Analytical Solutions of Two Space-Time Fractional Nonlinear Models Using Jacobi Elliptic Function Expansion Method

Rahman

Ali

Harun-Or-Roshid

2021

Contemporary Mathematics

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In this manuscript, the space-time fractional Equal-width (s-tfEW) and the space-time fractional Wazwaz-Benjamin-Bona-Mahony (s-tfWBBM) models have been investigated which are frequently arises in nonlinear optics, solid states, fluid mechanics and shallow water. Jacobi elliptic function expansion integral technique has been used to build more innovative exact solutions of the s-tfEW and s-tfWBBM nonlinear partial models. In this research, fractional beta-derivatives are applied to convert the partial models to ordinary models. Several types of solutions have been derived for the models and performed some new solitary wave phenomena. The derived solutions have been presented in the form of Jacobi elliptic functions initially. Persevering different conditions on a parameter, we have achieved hyperbolic and trigonometric functions solutions from the Jacobi elliptic function solutions. Besides the scientific derivation of the analytical findings, the results have been illustrated graphically for clear identification of the dynamical properties. It is noticeable that the integral scheme is simplest, conventional and convenient in handling many nonlinear models arising in applied mathematics and the applied physics to derive diverse structural precise solutions.

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“…Let us review the beta-derivative [21][22][23][24][25] as follows: Definition 1 Let ϕ : [a, ∞) → R, then the fractional beta-derivative of ϕ of order β is defined as…”

Section: Beta-fractional Derivativementioning

confidence: 99%

Section: Graphical Representationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analytical Solutions of Two Space-Time Fractional Nonlinear Models Using Jacobi Elliptic Function Expansion Method

Rahman

Ali

Harun-Or-Roshid

2021

Contemporary Mathematics

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“…The investigation of searching solutions for nonlinear integro differential equations plays an important role in nonlinear physical science, because the solutions can describe various natural phenomena of the problems such as wave traveling, vibrations, solitons, and propagation with a finite speed. Different researchers studied the practical and theoretical investigations of applications of partial differential equations [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Solutions of Nonlinear Integro-Partial Differential Equations by the Method of $(G^{'})$

Gusu

Bulo

2022

Advances in Mathematical Physics

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In this article, a special expansion method is implemented in solving nonlinear integro-partial differential equations of 2 + 1 -dimensional using a special expansion method of G ′ / G , 1 / G . We obtained the solutions for 2 + 1 -dimensional nonlinear integro-differential equations in real physical phenomena. The method is applied on 2 + 1 -dimensional space time and solved in three different cases: hyperbolic, trigonometric, and rational functions. The obtained solutions for each result were illustrated by graphical plots using Wolfram Mathematica 9.0 software packages. Furthermore, the obtained results are exactly fit with exact solutions which solves the complicity of finding the solution for nonlinear integro-partial differential equations. Finally, the method is powerful and effective to solve partial differential equations of nonlinear integro form.

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“…Especially, the study of traveling wave solutions of the Kaup-Boussinesq system have become a very important research feld [1][2][3][4][5][6]. Many important methods are also used to construct traveling wave solutions [7][8][9][10][11][12] and optical soliton solutions [13][14][15][16][17] of the Kaup-Boussinesq system. However, as far as we can tell from the literature, the solutions obtained mainly focus on hyperbolic function solutions, trigonometric function solutions, and rational function solutions.…”

Section: Introductionmentioning

confidence: 99%

Traveling Wave Solution of the Kaup–Boussinesq System with Beta Derivative Arising from Water Waves

Chen

2022

Discrete Dynamics in Nature and Society

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The main purpose of this paper is to construct the traveling wave solution of the Kaup–Boussinesq system with beta derivative arising from water waves. By using the complete discriminant system method of polynomial, the rational function solution, the trigonometric function solution, the exponential function solution, and the Jacobian function solution of the Kaup–Boussinesq system with beta derivative are obtained. In order to further explain the propagation of the Kaup–Boussinesq system with beta derivative in water waves, we draw its three-dimensional diagram, two-dimensional diagram, density plot, and contour plot by using Maple software.

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1-Soliton solutions of the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain model with the beta time derivative

Cited by 72 publications

References 42 publications

Analytical Solutions of Two Space-Time Fractional Nonlinear Models Using Jacobi Elliptic Function Expansion Method

Analytical Solutions of Two Space-Time Fractional Nonlinear Models Using Jacobi Elliptic Function Expansion Method

Solutions of Nonlinear Integro-Partial Differential Equations by the Method of $(G^{'})$

Traveling Wave Solution of the Kaup–Boussinesq System with Beta Derivative Arising from Water Waves

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1-Soliton solutions of the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain model with the beta time derivative

Cited by 72 publications

References 42 publications

Analytical Solutions of Two Space-Time Fractional Nonlinear Models Using Jacobi Elliptic Function Expansion Method

Analytical Solutions of Two Space-Time Fractional Nonlinear Models Using Jacobi Elliptic Function Expansion Method

Solutions of Nonlinear Integro-Partial Differential Equations by the Method of G ′

Traveling Wave Solution of the Kaup–Boussinesq System with Beta Derivative Arising from Water Waves

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Solutions of Nonlinear Integro-Partial Differential Equations by the Method of $(G^{'})$