The New Wave Solutions in the Field of Superconductivity

KIRCI, Özlem; Aktürk, Tolga

doi:10.17798/bitlisfen.1020207

Cited by 1 publication

(1 citation statement)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…LGHe (1.3) is used to understand the concepts of superconductivity and cyclotron waves, which have applications in a variety of fields, including medicine, plasma physics, chemistry, biology, electricity-electronics, and transportation [40].…”

Section: Introductionmentioning

confidence: 99%

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

Khalique,

Lephoko

2024

Commun. Theor. Phys.

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%