Single wave solutions of the fractional Landau-Ginzburg-Higgs equation in space-time with accuracy via the beta derivative and mEDAM approach

Ikram Ullah; Muhammad Bilal; Javed Iqbal; Hasan Bulut; Funda Turk; Ikram Ullah; Muhammad Bilal; Javed Iqbal; Hasan Bulut; Funda Turk

doi:10.3934/math.2025030

AIMS Mathematics

2025, Volume 10, Issue 1: 672-693. doi: 10.3934/math.2025030

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Research article

Single wave solutions of the fractional Landau-Ginzburg-Higgs equation in space-time with accuracy via the beta derivative and mEDAM approach

1.
School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China
2.
Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Khyber Pukhton Khwkha, Pakistan
3.
Department of Mathematics, Faculty of Science, Fırat University, Elazıg 23119, Türkiye
4.
Department of Mathematics, Faculty of Science, Bartın University, Bartın 74100, Türkiye

Received: 18 November 2024 Revised: 28 December 2024 Accepted: 30 December 2024 Published: 13 January 2025
MSC : 65F10, 65H10, 90C30, 90C33

The nonlinear wave behavior in the tropical and mid-latitude troposphere has been simulated using the space-time fractional Landau-Ginzburg-Higgs model. These waves are the consequence of interactions between equatorial and mid-latitude waves, fluid flow in dynamic systems, weak scattering, and extended linkages. The mEDAM method has been used to obtain new and extended closed-form solitary wave solutions of the previously published nonlinear fractional partial differential equation via the beta derivative. A wave transformation converts the fractional-order equation into an ordinary differential equation. Several soliton, single, kink, double, triple, anti-kink, and other soliton types are examples of known conventional wave shapes. The answers are displayed using the latest Python code, which enhances the usage of 2D and 3D plotlines, as well as contour plotlines, to emphasise the tangible utility of the solutions. The results of the study are clear, flexible, and easier to replicate.
- beta derivative,
- modified extended direct algebraic method,
- space-time fractional Landau-Ginzburg-Higgs equation,
- soliton solutions
Citation: Ikram Ullah, Muhammad Bilal, Javed Iqbal, Hasan Bulut, Funda Turk. Single wave solutions of the fractional Landau-Ginzburg-Higgs equation in space-time with accuracy via the beta derivative and mEDAM approach[J]. AIMS Mathematics, 2025, 10(1): 672-693. doi: 10.3934/math.2025030

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Abstract

The nonlinear wave behavior in the tropical and mid-latitude troposphere has been simulated using the space-time fractional Landau-Ginzburg-Higgs model. These waves are the consequence of interactions between equatorial and mid-latitude waves, fluid flow in dynamic systems, weak scattering, and extended linkages. The mEDAM method has been used to obtain new and extended closed-form solitary wave solutions of the previously published nonlinear fractional partial differential equation via the beta derivative. A wave transformation converts the fractional-order equation into an ordinary differential equation. Several soliton, single, kink, double, triple, anti-kink, and other soliton types are examples of known conventional wave shapes. The answers are displayed using the latest Python code, which enhances the usage of 2D and 3D plotlines, as well as contour plotlines, to emphasise the tangible utility of the solutions. The results of the study are clear, flexible, and easier to replicate.

References

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