New solitary wave solution for the nonlinear autonomous equations using an efficient method

Mohammed, Maha A.; Tawfiq, Luma N. M.

doi:10.47974/JIM-2563

Open Access Research Article

New solitary wave solution for the nonlinear autonomous equations using an efficient method

^*Maha A. MohammedCorresponding authormaha.aj.m@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Science (Ibn Al-Haitham)University of BaghdadBaghdad, IraqView full profile → , Luma N. M. Tawfiqluma.n.m@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Science (Ibn Al-Haitham)University of BaghdadBaghdad, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1697–1703Vol. 29Issue 5-BMay 2026DOI: 10.47974/JIM-2563XML

Received:: 01 Nov 2025
Published Online:: 27 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2563
Pages:: 1697–1703

Abstract

An efficient approach is used in this article to solve and analyze the nonlinear autonomous equations. The Tanh method provides more general, precise traveling wave solutions with little additional work. The Tanh technique is demonstrated to be an effective mathematical tool for solving nonlinear autonomous equations and any model equation in mathematical physics. Additionally, the obtained solutions are physically represented and interpreted. Furthermore, the authors present the visual effects of the behavior of wave structures using various figures and contour plots, in the results to enhance our comprehensive understanding.

Keywords

PDEs Soliton Breaking soliton Nonlinear autonomous equation Tanh method

Subject Classifications

37Dxx34Dxx76Fxx

References

[1] S. J. Mohammed and M. A. Mohammed, “Runge-kutta numerical method for solving nonlinear influenza model,” Journal of Physics: Conference Series, vol. 1879, no. 3, pp. 1–12 (2021).
[2] Z. H. Kareem, “Solving Three-Dimensional Groundwater Recharge Based on Decomposition Method,” Journal of Physics: Conference Series, vol. 1530, pp. 1–8 (2020).
[3] A. Q. Ibrahim Abed, “Efficient method for solving fourth order PDEs,” Journal of Physics: Conference Series, vol. 1818, no. 1, Art. no. 012166, pp. 1–10 (2021), doi: 10.1088/1742-6596/1818/1/012166.
[4] Z. H. Kareem, “Efficient Modification of the Decomposition Method for Solving a System of PDEs,” Iraqi Journal of Science, vol. 62, no. 9, pp. 3061–3070 (2021).
[5] Z. H. Kareem, “Recent modification of decomposition method for solving wave-like equation,” Journal of Interdisciplinary Mathematics, vol. 26, no. 5, pp. 809–820 (2023).
[6] F. F. Ghazi and L. N. M. Tawfiq, “Efficient design of neural network based on modified LM training algorithm for solving nonlinear 4th order 3D-PDEs,” Journal of Interdisciplinary Mathematics, vol. 29, no. 2, pp. 225–234 (2026), doi: 10.47974/JIM-2012.
[7] M. Enadi, “New Approach for Solving Three-Dimensional Space Partial Differential Equation,” Baghdad Science Journal, vol. 16, no. 3, pp. 786–792 (2019).
[8] F. F. Ghazi and L. N. M. Tawfiq, “New approach for solving two dimensional spaces PDE,” Journal of Physics: Conference Series, vol. 1530, no. 1, Art. no. 012066 (2020), doi: 10.1088/1742-6596/1530/1/012066.
[9] A. H. Khamas and L. N. Tawfiq, “New Approach for Calculate Exponential Integral Function,” Iraqi Journal of Science, vol. 64, no. 8, pp. 4034–4042 (2023).
[10] N. A. Hussein and L. N. M. Tawfiq, “Efficient approach for solving (2+1) D-differential equations,” Baghdad Science Journal, vol. 20, no. 1, pp. 166–174 (2023), doi: 10.21123/bsj.2022.6541.
[11] N. A. Hussein and L. N. Tawfiq, “Exact Solution for Systems of Nonlinear (2+1) D-Differential Equations,” Iraqi Journal of Science, vol. 63, no. 10, pp. 4388–4396 (2022).

Views: 62Downloads: 73Citations: 0