Construction of shock, periodic and solitary wave solutions for fractional-time Gardner equation by Jacobi elliptic function method

Elsadany, A. A.; Elboree, Mohammed. K.

doi:10.1007/s11082-023-06102-y

Opt Quant Electron

2024

DOI: 10.1007/s11082-023-06102-y

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Construction of shock, periodic and solitary wave solutions for fractional-time Gardner equation by Jacobi elliptic function method

A. A. Elsadany,

Mohammed. K. Elboree

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2024

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Cited by 4 publications

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Analyzing the Kuralay-II equation: bifurcation, chaos, and sensitivity insights through conformable derivative and Jacobi elliptic function expansion

Khan,

Farooq

2024

Phys. Scr.

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This study explores the intricate dynamics of the Kuralay-II equation by employing the conformable derivative. Using the Galilean transformation, we can establish a dynamical system related to the equation. We investigate bifurcation methods in this derived system using planar dynamical systems theory. By introducing a perturbed term, we thoroughly investigate the possibility of chaotic behaviors in the Kuralay-II equation using comprehensive two-phase portraiture. Through careful analysis, we have determined that even small changes in the initial conditions have little impact on the stability of the solution which has been confirmed by employing the Runge-Kutta method. In addition, we obtain exact solutions for the Kuralay-II equation by the Jacobi elliptic function expansion method. Graphical results of some solutions are showcased, offering a comprehensive evaluation using MATLAB across various dimensions. This study has yielded significant findings, such as the discovery of bifurcation points, the determination of conditions for chaos, and the analysis of stability under perturbations. These results have enhanced our understanding of the behavior of the Kuralay-II equation.

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Analyzing the Kuralay-II equation: bifurcation, chaos, and sensitivity insights through conformable derivative and Jacobi elliptic function expansion

Khan,

Farooq

2024

Phys. Scr.

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New periodic solutions and solitary wave solutions for the time-fractional differential equations

Liu,

Lu,

Chen

et al. 2024

Phys. Scr.

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In this paper, we obtain many diﬀerent types of exact solutions to the time-fractional Klein-Gordon equation and the time-fractional generalized Hirota-Satsuma coupled KdV system by using the modiﬁed rational function approach. Some new solutions such as the kink-periodic solution, the anti-kink-periodic solution and the concaveconvex-periodic solution are constructed. Furthermore, the kink and the singular kink waves, the soliton and the singular soliton solutions of the two equations also are found. Some numerical simulations are presented, these works can eﬀectively reﬂect the propagation phenomena of time-fractional nonlinear systems, and also enable us to understand time-fractional nonlinear physical phenomena more clearly.

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Numerical simulations and analytical approach for three-component coupled NLS-type equations in fiber optics

Abbas,

Shakeel,

Fouly

et al. 2024

Mod. Phys. Lett. B

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This work aims to look into the dynamic research of coupled NLS-type equations with three components. The optical solitons, including the periodic function, trigonometric function, exponential function, solitary wave, and elliptic function solutions are built using the Jacobi elliptic function (JEF) method. The investigations will aid in improving comprehension of the soliton dynamics system’s overall illustration. Using Mathematica software, we visually represent some solutions found in 3D, contour, and 2D graphs for tangible demonstration and visual presentation. These results are helpful in optical fiber, signal processing and data transmission.

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Construction of shock, periodic and solitary wave solutions for fractional-time Gardner equation by Jacobi elliptic function method

Cited by 4 publications

References 42 publications

Analyzing the Kuralay-II equation: bifurcation, chaos, and sensitivity insights through conformable derivative and Jacobi elliptic function expansion

Analyzing the Kuralay-II equation: bifurcation, chaos, and sensitivity insights through conformable derivative and Jacobi elliptic function expansion

New periodic solutions and solitary wave solutions for the time-fractional differential equations

Numerical simulations and analytical approach for three-component coupled NLS-type equations in fiber optics

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