A Numerical Comparison for Coupled nonlinear system by Adomian Decomposition Method

Authors

  • Najla J. Alawiss Department of Mathematics, Faculty of Science, Alasmarya Islamic University,Libya
  • Mariam. R. Abosetta Department of Mathematics, Faculty of Science, Alasmarya Islamic University,Libya
  • Huda Ali Aldweby Department of Mathematics, Faculty of Science, Alasmarya Islamic University,Libya

DOI:

https://doi.org/10.59743/

Keywords:

Coupled nonlinear system, ” Drinfel’d Sokolov Wilson equation” (DSWE) , "(Adomian Decomposition Method"(ADM

Abstract

 In this paper  we will study and  compare the numerical solutions by “Adomian Decomposition Method” (ADM) We obtained results from our work and compared them to the exact solution of the nonlinear coupled system known as the "Drinfel'd Sokolov Wilson equation"(DSWE), which is relevant in shallow water flows.

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References

Alhejeili, S., & Alharbi, A. (Year). Structure of Analytical and Numerical Wave Solutions for the Nonlinear (1 + 1)-Coupled Drinfel’d–Sokolov–Wilson System Arising in Shallow Water Waves.

Gurefe, Y., Sonmezoglu, A., & Misirli, E. (2011). Title of the Article. Pramana, Journal of Physics, 77 .(1023).

Liu, C. (2009). Title of the Article. Communications in Theoretical Physics, 45(219).

Misirli, E., & Gurefe, Y. (2010). Exact solutions of the Drinfel'd-Sokolov-Wilson Equation using the Exp-function method. Applied Mathematics and Computation, 216(9), 2623-2627.

Al-Askar, F. M., Cesarano, C., Mohammed, W. W. (2022). The Analytical Solutions of Stochastic-Fractional Drinfel’d-Sokolov-Wilson Equations via ( ´G/G)-Expansion Method. Symmetry, 14(2105).

Arnous, A. H., Mirzazadeh, M., Eslami, M. (2016). Exact solutions of the Drinfel'd-Sokolov-Wilson Equation using Backlund transformation of Riccati equation and trial function approach. Pramana, 86(6), 1153-1160.

Manaa, S. A. (2011). An Approximate Solution to The Newell-Whitehead Equation by Adomian Decomposition Method. Raf. Journal of Computation & Mathematics, 8(1).

Rao, T. R. R. (2010). The use of Adomian Decomposition Method for Solving Generalised Riccati Differential Equations. Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Application (ICMSA2010), University Tunku Abdul Rahman, Kuala Lumpur, Malaysia.

Drinfel’d, V. G., & Sokolov, V. V. (1981). Equations of Korteweg-de Vries type and simple Lie algebras. Soviet Mathematics Doklady, 23, 457–46..

Drinfel’d, V. G., & Sokolov, V. V. (1985). Lie algebras and equations of Korteweg-de Vries type. Journal of Soviet Mathematics, 30, 1975–200..

Hirota, R., Grammaticos, B., & Ramani, A. (1986). Soliton structure of the Drinfel’d-Sokolov-Wilson equation. Journal of Mathematical Physics, 27, 1499–150.

Zha, X. Q., & Zhi, H. Y. (2008). An Improved F·Expansion Method and Its Application to Coupled Drinfeld-Sokolov-Wilson Equation. Communications in Theoretical Physics, 50, 309-314.

Zhang, W.-M. (2011). Solitary Solutions and Singular Periodic Solutions of the Drinfeld-Sokolov-Wilson Equation by Variational Approach. Applied Mathematical Sciences, 5(38), 1887–1894.

Salerna, M. (1987). On the phase manifold geometry of the two-dimensional Burgers equation. Physics Letters A, 121, 15-18.

Kaya, D., Yokus, A. (2005). A decomposition method for finding solitary and periodic solutions for a coupled higher-dimensional Burgers equations. Applied Mathematics and Computations, 164(3), 857-864

Zubair, T., Usman, M., Ali, U., Mohyud-Din, S. T. (2012). Homotopy Analysis Method for System of Partial Differential Equations. International Journal of Modern Engineering Sciences, 1(2), 67-79

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Published

28-07-2025

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Section

Applied Sciences

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How to Cite

Alawiss, N. J., Abosetta, M. R. ., & Aldweby, H. A. . (2025). A Numerical Comparison for Coupled nonlinear system by Adomian Decomposition Method. Journal of the Academic Forum, 9(2), 241-253. https://doi.org/10.59743/