New Exact Solutions of Landau-Ginzburg-Higgs Equation Using Power Index Method

Ahmad, Khalid; Bibi, Khudija; Arif, Muhammad; Abodayeh, Kamaleldin

doi:10.1155/2023/4351698

Cited by 11 publications

(3 citation statements)

References 13 publications

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“…-expansion method to gain traveling wave solutions. Recently, Ahmad et al [44] obtained exact solutions of the LGHe in terms of elliptic Jacobi functions by applying the power index method using function conversion. Asjad et al [45] obtained solitary wave solitons by utilizing the generalized projective Riccati method.…”

Section: Introductionmentioning

confidence: 99%

Conserved vectors and symmetry solutions of the Landau–Ginzburg–Higgs equation of theoretical physics

Khalique,

Lephoko

2024

Commun. Theor. Phys.

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This paper is devoted to the investigation of the Landau-Ginzburg-Higgs equation (LGHe), which serves as a mathematical model to understand phenomena such as superconductivity and cyclotron waves. The LGHe finds applications in various scientific fields, including fluid dynamics, plasma physics, biological systems, and electricity-electronics. The study adopts Lie symmetry analysis as the primary framework for exploration. This analysis involves the identification of Lie point symmetries that are admitted by the differential equation. By leveraging these Lie point symmetries, symmetry reductions are performed, leading to the discovery of group invariant solutions. To obtain explicit solutions, several mathematical methods are applied, including Kudryashov's method, the extended Jacobi elliptic function expansion method, the power series method, and the simplest equation method. These methods yield solutions characterized by exponential, hyperbolic, and elliptic functions. The obtained solutions are visually represented through 3D, 2D, and density plots, which effectively illustrate the nature of the solutions. These plots depict various patterns such as kink-shaped, singular kink-shaped, bell-shaped, and periodic solutions. Finally, the paper employs the multiplier method and the conservation theorem introduced by Ibragimov to derive conserved vectors. These conserved vectors play a crucial role in studying physical quantities, such as the conservation of energy and momentum, and contribute to the understanding of the underlying physics of the system.

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Section: Introductionmentioning

confidence: 99%

Conserved vectors and symmetry solutions of the Landau–Ginzburg–Higgs equation of theoretical physics

Khalique,

Lephoko

2024

Commun. Theor. Phys.

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“…Similarly, for the nonlinear Landau-Ginzburg-Higgs (LGH) equation, Kundu et al 20 applied the Sine-Gordon expansion procedure to obtain exact solutions, while Barman et al 21,22 examined the same equation using the Kudryashov technique and the extended tanh-function process to derive exact wave results. Additionally, Ahmad et al 23 applied the power index approach to study this model.…”

Section: Introductionmentioning

confidence: 99%

New Traveling Wave Solutions to the Simplified Modified Camassa–Holm Equation and the Landau-Ginsburg-Higgs Equation

Sagib,

Ghosh,

Roy

2024

Dhaka Univ. J. Sci.

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Researchers are interested in the (1+1)-dimensional Camassa-Holm and Landau-Ginzburg-Higgs equations as they allow for the study of unidirectional wave propagation in shallow waters with a flat seabed, as well as nonlinear media exhibiting dispersion systems and superconductivity. This work has effectively developed exact wave solutions to the stated models, which may have significant consequences for characterising the nonlinear dynamical behaviour related to the phenomena. The extended -expansion technique is employed to procure a diverse array of progressive wave solutions characterized by hyperbolic, trigonometric, and rational functions. The solutions are shown as 3D profiles with a variety of shapes, including kink, singular kink, periodic, singular periodic, etc. The physical significance of the solutions is discussed by these plots, and the approach used in this study is considered efficient and capable of finding analytical solutions for the nonlinear models. Dhaka Univ. J. Sci. 72(1): 7-13, 2024 (January)

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“…The inverse wave scattering method is used and travelling wave solutions of the LGH model are analyzed [20]. Furthermore, using power index technique some exact solutions of the LGH equation are studied [21].…”

Section: Introductionmentioning

confidence: 99%

Analysing the Landau-Ginzburg-Higgs equation in the light of superconductivity and drift cyclotron waves: Bifurcation, chaos and solitons

Ahmad,

Lou,

Khan

et al. 2023

Phys. Scr.

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The Landau-Ginzburg-Higgs (LGH) equation is a fundamental framework for examining physical systems in the fields of condensed matter physics and field theory. This study delves into the LGH equation, particularly in the context of its relevance to superconductivity and drift cyclotron waves. Researchers have extensively investigated the LGH equation to uncover a diverse array of exact solutions, employing various methodologies. This manuscript centers on the examination of its dynamic properties, encompassing the analysis of phenomena such as bifurcations, sensitivity, chaotic behavior, and the emergence of soliton solutions. To achieve this, we employ the principles of planar dynamical theory, shedding light on the intricate behaviors embedded within the LGH equation. Furthermore, we utilize the tools and techniques provided by planar dynamical theory to derive soliton solutions for the LGH equation.

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New Exact Solutions of Landau-Ginzburg-Higgs Equation Using Power Index Method

Cited by 11 publications

References 13 publications

Conserved vectors and symmetry solutions of the Landau–Ginzburg–Higgs equation of theoretical physics

Conserved vectors and symmetry solutions of the Landau–Ginzburg–Higgs equation of theoretical physics

New Traveling Wave Solutions to the Simplified Modified Camassa–Holm Equation and the Landau-Ginsburg-Higgs Equation

Analysing the Landau-Ginzburg-Higgs equation in the light of superconductivity and drift cyclotron waves: Bifurcation, chaos and solitons

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