Unveiling the Dynamics of Nonlinear Landau-Ginzburg-Higgs (LGH) Equation: Wave Structures through Multiple Auxiliary Equation Methods

Year 2024, Issue: 48, 11 - 23, 30.09.2024

Şerife Müge Ege

https://doi.org/10.53570/jnt.1506419

Abstract

This comprehensive investigation delves deeply into the intricate dynamics governed by the nonlinear Landau-Ginzburg-Higgs equation. It uncovers a diversity of semi-analytical solutions by leveraging three auxiliary equation methods within the traveling wave framework. This article effectively utilizes the improved Kudryashov, Kudryashov's R, and Sardar's subequation methods. The methods discussed are advantageous because they are easy to implement and suitable for use with the Mathematica package program. Each method yields a distinct set of solutions, scrutinized across all cases. We elucidate the complex wave structures through 3D, 2D, and contour graphical representations, providing profound insights into their underlying characteristics. Furthermore, we scrutinize the influence of parameter variations on these wave structures, thereby offering a comprehensive understanding of their dynamic behavior.

Keywords

Landau-Ginzburg-Higgs equation, improved Kudryashov method, Kudryashov, Sardar

Ethical Statement

The author read and approved the final version of the paper. The author declares no conflict of interest.

Supporting Institution

Ege University

Project Number

BAP24004

Thanks

This study was supported by the Office of Scientific Research Projects Coordination at Ege University, Grant number: 24004.

References

• A. M. Shahoot, K. A. E. Alurrfi, M. O. M. Elmrid, A. M. Almsiri, A. M. H. Arwiniya, The expansion method for solving a nonlinear PDE describing the nonlinear low-pass electrical lines, Journal of Taibah University for Science 13 (1) (2019) 63-70.
• S. Akcagil, T. Aydemir, Comparison between the expansion method and the modified extended tanh method, Open Physics 14 (2016) 88-94.
• N. Aminakbari, Y. Gu, W. Yuan, Bernoulli-expansion method for nonlinear Schrodinger equation under effect of constant potential, Optical and Quantum Electronics 53 (331) (2021) 1-11.
• L. Akinyemi, M. Senol, O. S. Iyiola, Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method, Mathematics and Computers in Simulation 182 (2021) 211-233.
• H. Durur, A. Kurt, O. Tasbozan, New traveling wave solutions for KdV equation using sub equation method, Applied Mathematics and Nonlinear Sciences 5 (1) (2020) 455-460.
• L. Yan, H. M. Baskonus, C. Cattani, W. Gao, Extraction of the gravitational potential and high-frequency wave perturbation properties of nonlinear (3+1)-dimensional Vakhnenko Parkes equation via novel approach, Mathematical Methods in the Applied Sciences 5 (1) (2022) 1-10.
• S. B. Yamgoue, G. R. Deffo, F. B. Pelap, A new rational sine-Gordon expansion method and its application to nonlinear wave equations arising in mathematical physics, The European Physical Journal Plus 134 (380) (2019) 1-15.
• E. Misirli, Y. Gurefe, Exp-function method for solving nonlinear evolution equations, Mathematical and Computational Applications 16 (1) (2011) 258-266.
• T. Akturk, G. Yel, Modified exponential function method for the KP-BBM equation, Mathematics in Natural Science 6 (2020) 1-7.
• O. Kirci, T. Akturk, H. Bulut, Simulation of wave solutions of a mathematical model representing communication signals, Journal of the Institute of Science and Technology 11 (4) (2021) 3086-3097.
• M. Ekici, M. Unal, Application of the exponential rational function method to some fractional soliton equations, Emerging Applications of Differential Equations and Game Theory (2020) 13-32.
• B. Ghanbari, M. S. Osman, D. Baleanu, Generalized exponential rational function method for extended Zakharov-Kuzetsov equation with conformable derivative, Modern Physics Letters A 34 (20) (2019) 1-16.
• S. Akcagil and T. Aydemir, A new application of the unified method, New Trends in Mathematical Sciences 6 (2018) 185-199.
• N. Raza, M. H. Rafiq, M. Kaplan, S. Kumar, Y. M. Chu, The unified method for abundant soliton solutions of local time fractional nonlinear evolution equations, Results in Physics 22 (20) (2021) 1-7.
• A. N. Kudryashov, One method for finding exact solutions of nonlinear differential equations, Communications in Nonlinear Science and Numerical Simulation 17 (2012) 2248-2253.
• M. Kaplan, A. Bekir, A. Akbulut, A generalized Kudryashov method to some nonlinear evolution equations in mathematical physics, Nonlinear Dynamics 85 (2016) 2843-2850.
• S. M. Ege, Traveling wave solutions for two physical models via extended modified Kudryashov method, Journal of the Institute of Science and Technology 11 (1) (2021) 625-634.
• N. A. Kudryashov, Method for finding highly dispersive optical solitons of nonlinear differential equations, Optik International Journal for Light and Electron Optics 206 (2020) 1-9.
• N. A. Kudryashov, Solitary waves of the non-local Schrodinger equation with arbitrary refractive index, Optik 231 (2021) 1-5.
• S. Bibi, S. T. Mohyud-Din, U. Khan, N. Ahmed, Khater method for nonlinear Sharma Tasso-Olever (STO) equation of fractional order, Results in Physics 7 (2017) 4440-4450.
• S. Yao, E. Ilhan, P. Veeresha, H. M. Baskonus, A powerful iterative approach for quintic complex Ginzburg–Landau equation within the frame of fractional operator, Fractals 29 (2021) 1-13.
• F. Yuan, B. Ghanbari, A study of interaction soliton solutions for the (2+1)-dimensional Hirota-Satsuma-Ito equation, Nonlinear Dynamics 112 (2024) 2883-2891.
• H. K. Barman, M. A. Akbar, M. S. Osman, K. S. Nisar, M. Zakarya, A. H. Abdel-Aty, H. Eleuch, Solutions to the Konopelchenko-Dubrovsky equation and the Landau-Ginzburg-Higgs equation via the generalized Kudryashov technique, Results in Physics 24 (2021) 1-10.
• L. Akinyemi, P. Veeresha, M. T. Darvishi, H. Rezazadeh, M. Senol, U. Akpan, A novel approach to study generalized coupled cubic Schrödinger–Korteweg-de Vries equations, Journal of Ocean Engineering and Science 9 (2024) 13-24.