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RESEARCH ARTICLE

An analytical investigation of the wave propagation behavior of the truncated M-fractional Landau–Ginzburg–Higgs model through two consent techniques

M. Al Amin1∗ ,  M. Nurul Islam1 ,  M. Ali Akbar2
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1 Department of Mathematics, Faculty of Sciences, Islamic University, Kushtia, Khulna, Bangladesh
2 Department of Applied Mathematics, Faculty of Science, University of Rajshahi, Rajshahi, Bangladesh
NSCE, 025290004 https://doi.org/10.36922/NSCE025290004
Received: 20 July 2025 | Revised: 17 September 2025 | Accepted: 9 October 2025 | Published online: 14 November 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

The nonlinear fractional Landau–Ginzburg–Higgs (LGH) model is a renowned nonlinear integrable mathematical model that is used to explain the nonlinear signal that shows weak scattering and radial links in the tropical and mid-latitude troposphere as interplays between equatorial and mid-latitude Rossby waves, superconductivity, and drift cyclotron waves in radially inhomogeneous plasma for coherent ion-cyclotron waves and equivalent incidents. This article investigates the fractional order of the LGH model utilizing two recent schemes: the generalized exponential rational function method and the extended tanh-function method, incorporating the truncated M-fractional derivative. Using these methods, we obtained a large number of different types of traveling wave solutions, including exponential functions, hyperbolic functions, trigonometric functions, rational functions, and their composite functions. Moreover, we examined the influence of wave velocity parameters on the soliton by sketching three-dimensional, along with two-dimensional plots of the obtained results. The attainment outcome authenticates the effectiveness and consistency of the utilized methods. The appropriateness of the obtained solutions is settled by putting them into their original model.

Keywords
Extended tanh-function method
Generalized exponential rational function method
Nonlinear fractional Landau–Ginzburg–Higgs (LGH) model
Soliton solution
Truncated M-fractional derivative
Funding
None.
Conflict of interest
The authors declare they have no competing interests.
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