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Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

Variational iteration method for solving generalized complex Ginzburg-Landau equation

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pp. 51–58Vol. 28Issue 1February 2025DOI: 10.47974/JIM-1775XML
Received:
06 Jun 2024
Published Online:
13 Feb 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-1775
Pages:
51–58

Abstract

This study investigates the application of the variational iterative method (VIM) to solve the nonlinear complex Ginzburg-Landau problem. This study investigates the use of VIM to solve the complex nonlinear Ginzburg-Landau problem. Using MATLAB, a powerful scientific computing program, the study develops a algorithm based on VIM principles to solve probable solutions that recur to convergence and tests this approach if in four cases it shows high accuracy and efficiency for solving complex equations.

Keywords

Subject Classifications

Primary 35GxxSecondary 35G25

References

[1] M. R. Farahani, S. Jafari, S. A. Mohiuddine, and M. Cancan, “Intuitionistic fuzzy stability of generalized additive set-valued functional equation via fixed point method,” Mathematical Statistician and Engineering Applications, vol. 71, no. 3s3, pp. 142–154 (2022). [Online]. Available: https://doi.org/10.17762/msea.v71i3s3.355.
[2] W. Gao and M. R. Farahani, “The hyper-Zagreb index for an infinite family of nanostar dendrimer,” Journal of Discrete Mathematics, Sciences and Cryptography, vol. 20, no. 2, pp. 515–523 (2017). [Online]. Available: https://doi.org/10.1080/09720529.2016.1220088.
[3] W. Gao and M. R. Farahani, “The Zagreb topological indices for a type of Benzenoid systems jagged-rectangle,” Journal of Interdisciplinary Mathematics, vol. 20, no. 5, pp. 1341–1348 (2017). [Online]. Available: https://doi.org/10.1080/09720502.2016.1232037.
[4] W. Gao, L. Shi, and M. R. Farahani, “Szeged related indices of TUAC6[p, q],” Journal of Discrete Mathematics, Sciences and Cryptography, vol. 20, no. 2, pp. 553–563 (2017). [Online]. Available: https://doi.org/10.1080/09720529.2016.1228312.
[5] X. Zhang, A. Razzaq, K. Ali, S. T. R. Rizvi, and M. R. Farahani, “A new approach to find eccentric indices of some graphs,” Journal of Informational and Optimization Sciences, vol. 41, no. 4, pp. 865–877 (2020). [Online]. Available: https://doi.org/10.1080/02522667.2020.1744304.
[6] A. Al-Haboobi and A. H. Al-Muslimawi, “Novel algorithm for compressible Newtonian axisymmetric thermal flow,” International Journal of Modern Physics C, vol. 2450025, pp. 17 (2024). [Online]. Available: https://doi.org/10.1142/S0129183124500256.
[7] A. Al-Haboobi, G. A. Al-Juaifri, and A. H. Al-Muslimawi, “Numerical study of Newtonian laminar flow around circular and square cylinders,” Results in Control and Optimization, vol. 100328 (2023). [Online]. Available: https://doi.org/10.1016/j.rico.2023.100328.
[8] Mechee, M. S., Al-Shaher, O. I., & Al-Juaifri, G. A. Haar wavelet technique for solving fractional differential equations with an application. In AIP Conference Proceedings (Vol. 2086, No. 1). AIP Publishing (2019, April).
[9] A. K. Joohy, G. A. Al-Juaifri, and M. S. Mechee, “An investigation of solving third-order nonlinear ordinary differential equation in complex domain by generalizing Prelle-Singer method,” International Journal of Differential Equations, vol. 2020, pp. 1–9 (2020). [Online]. Available: https://doi.org/10.1155/2020/5276024.
[10] S. Wang and L. Z., “An efficient split-step compact finite difference method for cubic-quintic complex Ginzburg-Landau equations,” Computer Physics Communications, vol. 184, no. 6, pp. 1511–1521 (2013). [Online]. Available: https://doi.org/10.1016/j.cpc.2013.01.019.
[11] J. M. Soto-Crespo, N. N. Akhmediev, and V. V. Afanasjev, “Stability of the pulselike solutions of the quintic complex Ginzburg-Landau equation,” Journal of the Optical Society of America B, vol. 13, no. 7, pp. 1439–1449 (1996). [Online]. Available: https://doi.org/10.1364/JOSAB.13.001439.
[12] W. Liu, X. Zhang, Y. Li, L. Yan, and A. Q. Baig, “Analytic solutions for the generalized complex Ginzburg-Landau equation in fiber lasers,” Nonlinear Dynamics, vol. 89, pp. 2933–2939 (2017). [Online]. Available: https://doi.org/10.1007/s11071-017-3636-5.
[13] M. A. Isah and A. Yokuş, “Optical solitons of the complex Ginzburg-Landau equation having dual power nonlinear form using φ^6-model expansion approach,” Mathematical Modelling and Numerical Simulation with Applications, vol. 3, no. 3, pp. 188–215 (2023). [Online]. Available: https://doi.org/10.53391/mmnsa.1337648.
[14] A. Zafar, M. M. R. Laghari, A. T. M. Nazari, M. H. Shakir, and S. Zubair, “Analytical study of complex Ginzburg-Landau equation arising in nonlinear optics,” Journal of Nonlinear Optical Physics & Materials, vol. 32, no. 01, pp. 2350010 (2023). [Online]. Available: https://doi.org/10.1142/S0218863523500108.
[15] A. H. Arnous, N. S. Malik, M. S. Anwar, and Z. Y. Zhang, “Cubic-quartic optical solitons of the complex Ginzburg-Landau equation: A novel approach,” Nonlinear Dynamics, vol. 2023, pp. 1–16. [Online]. Available: https://doi.org/10.1007/s11071-023-08854-4.
[16] M. A. Isah and A. Yokuş, “The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity,” Mathematical Modelling and Numerical Simulation with Applications, vol. 2, no. 3, pp. 147–163 (2022). [Online]. Available: https://doi.org/10.53391/mmnsa.2022.012.
[17] J. H. He, “Variational iteration method—a kind of non-linear analytical technique: Some examples,” International Journal of Nonlinear Mechanics, vol. 34, no. 4, pp. 699–708 (1999). [Online]. Available: https://doi.org/10.1016/S0020-7462(98)00048-1.
[18] G. A. Al-Juaifri, A. Al-Haboobi, and J. M. Al-Ghabban, “Programming variational iteration method via Wolfram Mathematica for solving multi-order differential equations,” International Journal of Applied Mathematics, vol. 32, no. 5, pp. 785 (2019). [Online]. Available: https://doi.org/10.12732/ijam.v32i5.6.
[19] M. A. Abdou and A. A. Soliman, “New applications of variational iteration method,” Physica D: Nonlinear Phenomena, vol. 211, no. 1-2, pp. 1–8 (2005). [Online]. Available: https://doi.org/10.1016/j.physd.2005.08.002.
[20] X. Zhang, F. A. Shah, Y. Li, L. Yan, A. Q. Baig, and M. R. Farahani, “A family of fifth-order convergent methods for solving nonlinear equations using variational iteration technique,” Journal of Informational and Optimization Sciences, vol. 39, no. 3, pp. 673–694 (2018). [Online]. Available: https://doi.org/10.1080/02522667.2018.1443628.

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