New Analytical Wave Structures for the (2+1)-Dimensional Chaffee-Infante Equation

Year 2025, Volume: 8 Issue: 1, 41 - 55, 25.03.2025

Fatma Nur Kaya Sağlam

https://doi.org/10.32323/ujma.1633133

Abstract

The focus of this paper is the (2+1)-dimensional Chaffee-Infante equation (CIE). The model describes the diffusion of a gas in a homogeneous medium, which makes it an important tool in the research of mathematics and physics. The modified extended Tanh expansion method is employed. Many soliton solutions have been obtained by rigorous analysis and calculation. This method can generate various types of solutions including trigonometric, trigonometric-hyperbolic, rational, kink, singular, and periodic singular solitons. We also present some of the obtained solutions' 3D, contour, and 2D plots. In order to tackle complex nonlinear issues, the solutions are dependable, efficient, and manageable, and the generated results provide a basis for further research. The study's method used in this paper is characterised by its ability to generate simple, reliable and original solutions to nonlinear partial differential equations (NLPDEs) in mathematical physics. To the best of our knowledge, no such work has been done before for this problem. The Maple software has been used to check the correctness of each solution found.

Keywords

(2+1)-dimensional Chaffee-Infante equation, Modified extended Tanh expansion method, Solitons

References

• [1] H. Wang, X. Wu, X. Zheng, X. Yuan, Model predictive current control of nine-phase open-end winding PMSMs with an online virtual vector synthesis strategy, IEEE Trans. on Indust. Electronics, 70(3) (2022), 2199-2208.
• [2] W. B. Rabie, H. M. Ahmed, A. R. Seadawy, A. Althobaiti, The higher-order nonlinear Schrödinger’s dynamical equation with fourth-order dispersion and cubic-quintic nonlinearity via dispersive analytical soliton wave solutions, Opt. Quantum Electron., 53 (2021), 1-25.
• [3] M. A. Ravindran, K. Nallathambi, P. Vishnuram, R. S. Rathore, M. Bajaj, I. Rida, A. Alkhayyat, A novel technological review on fast charging infrastructure for electrical vehicles: Challenges, solutions, and future research directions, Alex. Eng. J., 82 (2023), 260-290.
• [4] N. Farah, A. R. Seadawy, S. Ahmad, S. T. Rizvi, Butterfly, S and W-shaped, parabolic, and other soliton solutions to the improved perturbed nonlinear Schrödinger equation, Opt. Quantum Electron., 55(1) (2023), 99.
• [5] Y. Li, H. Wang, M. Trik, Design and simulation of a new current mirror circuit with low power consumption and high performance and output impedance, Analog Integr. Circuits Signal Process., 119(1) (2024), 29-41.
• [6] J. Y. Gao, J. Liu, H. M. Yang, H. S. Liu, G. Zeng, B. Huang, Anisotropic medium sensing controlled by bound states in the continuum in polarization independent metasurfaces, Opt. Express, 31(26) (2023), 44703-44719.
• [7] D. Baleanu, S. M. Aydogn, H. Mohammadi, S. Rezapour, On modelling of epidemic childhood diseases with the Caputo-Fabrizio derivative by using the Laplace Adomian decomposition method, Alex. Eng. J., 59(5) (2020), 3029-3039.
• [8] F. Jarad, A. Jhangeer, J. Awrejcewicz, M. B. Riaz, M. Junaid-U-Rehman, Investigation of wave solutions and conservation laws of generalized Calogero–Bogoyavlenskii–Schiff equation by group theoretic method, Results Phys., 37 (2022), 105479.
• [9] Y. Pandir, A. Ekin, New solitary wave solutions of the Korteweg-de Vries (KdV) equation by new version of the trial equation method, Electron. J. Appl. Math., 1(1) (2023), 101-113.
• [10] Y. Yıldırım, A. Biswas, A. Dakova, P. Guggilla, S. Khan, H. M. Alshehri, M. R. Belic, Cubic-quartic optical solitons having quadratic-cubic nonlinearity by sine-Gordon equation approach, Ukr. J. Phys. Opt., 22(4) (2021), 255-269.
• [11] B. Kopçasız, Unveiling New Exact Solutions of the Complex-Coupled Kuralay System Using the Generalized Riccati Equation Mapping Method, J. Math. Sci. Model., 7(3) (2024), 146-156.
• [12] F. N. K. Sağlam, S. Malik, Various traveling wave solutions for (2+ 1)-dimensional extended Kadomtsev–Petviashvili equation using a newly created methodology, Chaos Solitons Fractals, 186 (2024), 115318.
• [13] B. Kopçasız, E. Yaşar, Solitonic structures and chaotic behavior in the geophysical Korteweg–de Vries equation: A $\mu$-symmetry and $g'$-expansion approach, Mod. Phys. Lett. B., (2024), 2450419.
• [14] B. Kopçasız, E. Yaşar, Adaptation of Caputo residual power series scheme in solving nonlinear time fractional Schr¨odinger equations, Optik, 289 (2023), 171254.
• [15] H. Durur, A. Kurt, O. Tasbozan, New travelling wave solutions for KdV6 equation using sub equation method, Appl. Math. Nonlinear Sci., 5(1) (2020), 455-460.
• [16] V. Ala, G. Shaikhova, Analytical solutions of nonlinear Beta fractional Schr¨odinger equation via Sine-Cosine method, Lobachevskii J. Math., 43(11) (2022), 3033-3038.
• [17] B. Inan, M. S. Osman, T. Ak, D. Baleanu, Analytical and numerical solutions of mathematical biology models: The Newell-Whitehead-Segel and Allen-Cahn equations, Math. Methods Appl. Sci., 43(5) (2020), 2588-2600.
• [18] J. Lenells, Traveling wave solutions of the Camassa–Holm equation, J. Differential Equations, 217(2) (2005), 393-430.
• [19] T. A. Sulaiman, A. Yusuf, M. Alquran, Dynamics of lump solutions to the variable coefficients (2+ 1)-dimensional Burger’s and Chaffee-infante equations, J. Geom. Phys., 168 (2021), 104315.
• [20] C. Zhu, M. Al-Dossari, S. Rezapour, B. Gunay, On the exact soliton solutions and different wave structures to the (2+ 1) dimensional Chaffee–Infante equation, Results Phys., 57 (2024), 107431.
• [21] M. A. Akbar, N. H. M. Ali, J. Hussain, Optical soliton solutions to the (2+ 1)-dimensional Chaffee–Infante equation and the dimensionless form of the Zakharov equation, Adv. Difference Equ., 2019(1) (2019), 446.
• [22] N. G. Ay, E. Yaşar, The residual symmetry, Backlund transformations, CRE integrability and interaction solutions:(2+ 1)-dimensional Chaffee–Infante equation, Commun. Theor. Phys., 75(11) (2023), 115004.
• [23] H. Esen, M. Ozisik, A. Secer, M. Bayram, Optical soliton perturbation with Fokas–Lenells equation via enhanced modified extended tanh-expansion approach, Optik, 267 (2022), 169615.
• [24] Y. Mao, Exact solutions to (2+ 1)-dimensional Chaffee–Infante equation, Pramana, 91(1) (2018), 9.
• [25] D. Chen, Q. Wang, Y. Li, Y. Li, H. Zhou, Y. Fan, A general linear free energy relationship for predicting partition coefficients of neutral organic compounds, Chemosphere, 247 (2020), 125869.
• [26] C. Zhu, M. Al-Dossari, N. S. A. El-Gawaad, S. A. M. Alsallami, S. Shateyi, Uncovering diverse soliton solutions in the modified Schrödinger’s equation via innovative approaches, Results Phys., 54 (2023), 107100.
• [27] D. Chen, Y. Li, X. Li, X. Hong, X. Fan, T. Savidge, Key difference between transition state stabilization and ground state destabilization: increasing atomic charge densities before or during enzyme-substrate binding, Chem. Sci., 13(27) (2022), 8193-8202.
• [28] M. Bilal, J. Iqbal, R. Ali, F. A. Awwad, E. A. Ismail, Exploring families of solitary wave solutions for the fractional coupled Higgs system using modified extended direct algebraic method, Fractal Fract., 7(9) (2023), 653.