Bifurcation Analysis and Soliton Solutions to the Kuralay Equation Via Dynamic System Analysis Method and Complete Discrimination System Method

Liu, Jing; Li, Zhao

doi:10.1007/s12346-024-00990-5

Cited by 7 publications

(2 citation statements)

References 64 publications

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“…Equation (5) simplifies to the following form. (36) with equation (4) into equation (25) yields the following set of equation…”

Section:  Umentioning

confidence: 99%

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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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“…Equation (5) simplifies to the following form. (36) with equation (4) into equation (25) yields the following set of equation…”

Section:  Umentioning

confidence: 99%

“…Applying the previously described method to solve the problem and incorporating the value involves in equation (36), we successfully derived the exact solution for the Kuralay-IIA equation with conformable derivative. With …”

mentioning

confidence: 99%

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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Dynamical behavior of analytical soliton solutions to the Kuralay equations via symbolic computation

Hussain,

Ibrahim,

Birkea

et al. 2024

Nonlinear Dyn

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Exploring the non-classical symmetry, bifurcation with sensitivity analysis of a (3 + 1)-dimensional nonlinear evolution equation

Alazman,

Mishra,

Alkahtani

et al. 2025

Ain Shams Engineering Journal

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Bifurcation Analysis and Soliton Solutions to the Kuralay Equation Via Dynamic System Analysis Method and Complete Discrimination System Method

Cited by 7 publications

References 64 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

Dynamical behavior of analytical soliton solutions to the Kuralay equations via symbolic computation

Exploring the non-classical symmetry, bifurcation with sensitivity analysis of a (3 + 1)-dimensional nonlinear evolution equation

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Bifurcation Analysis and Soliton Solutions to the Kuralay Equation Via Dynamic System Analysis Method and Complete Discrimination System Method

Cited by 7 publications

References 64 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

Dynamical behavior of analytical soliton solutions to the Kuralay equations via symbolic computation

Exploring the non-classical symmetry, bifurcation with sensitivity analysis of a (3 + 1)-dimensional nonlinear evolution equation

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Product

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Exploring the non-classical symmetry, bifurcation with sensitivity analysis of a (3 + 1)-dimensional nonlinear evolution equation