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Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

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Open Access Research Article

Traveling wave solutions to the class of nonlinear partial differential equations with a Riccati-Bernoulli sub-ODE method

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pp. 2781–2794Vol. 28Issue 8December 2025DOI: 10.47974/JIM-2147XML
Received:
05 Mar 2024
Published Online:
15 Oct 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2147
Pages:
2781–2794

Abstract

This research investigates the application of the Riccati-Bernoulli (R-B) sub-ODE technique to analyze the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP)  and the three-dimensional Potential Yu-Toda-Sasa-Fukuyama (3D-PYTSF) equations. By integrating traveling wave transformations with the R-B framework, both equations are systematically reduced to algebraic systems. Various soliton solutions, including kink-type, singular, and periodic solutions, are derived. To visualize the physical significance of these solutions, 3D plots, density graphs, and contour diagrams are generated based on appropriate parameter selections. The R-B sub-ODE method proves to be an effective yet straightforward technique for addressing nonlinear partial differential equations (NLPDEs).

Keywords

Subject Classifications

35Q51

References

[1] M. Alquran, S. Al Shara, and S. Al-Nimrat, “Kink, singular soliton, and periodic solutions to a class of nonlinear equations,” Applications and Applied Mathematics, vol. 10, pp. 212–222 (2015).
[2] S. Ibrahim, “Optical soliton solutions for the nonlinear third-order partial differential equation,” Advances in Differential Equations and Control Processes, vol. 29, pp. 127–138 (2022).
[3] A. R. Alharbi and M. B. Almatrafi, “Riccati-Bernoulli sub-ODE approach on the partial differential equations and applications,” International Journal of Mathematics and Computer Science, vol. 15, no. 1, pp. 367–388 (2020).
[4] M. Younis, S. Ali, and S. A. Mahmood, “Solitons for compound Kdv Burgers equation with variable coefficients and power law nonlinearity,” Nonlinear Dynamics, vol. 81, pp. 1192–1196 (2015).
[5] M. M. Al Quraishi, A. Yusuf, A. I. Aliyu, and M. Inc, “Optical and other solitons for fourth-order dispersive nonlinear Schrödinger equation with dual power law nonlinearity,” Superlattices and Microstructures, vol. 105, pp. 183–197 (2017).
[6] W. Malfliet and W. Hereman, “The tanh method: Exact solutions of nonlinear evolution and wave equations,” Physica Scripta, vol. 54, pp. 563–568 (1996).
[7] A. M. Wazwaz, “The tanh method for traveling wave solutions of non-linear equations,” Applied Mathematics and Computation, vol. 154, pp. 714–723 (2004).
[8] L. Ali, S. Islam, T. Gul, and I. Khan, “New version of optimal homotopy asymptotic method for the solution of nonlinear boundary value problems in finite and infinite intervals,” Alexandria Engineering Journal, vol. 55, pp. 2811–2819 (2016).
[9] L. Ali, S. Islam, T. Gul, A. S. Alshomrani, I. Khan, and A. Khan, “Magnetohydrodynamics thin film fluid flow under the effect of thermophoresis and variable fluid properties,” AIChE Journal (2017), doi: 10.1002/aic.15794.
[10] J. Ali, S. Islam, H. Khan, and S. I. Shah, “The optimal homotopy asymptotic method for the solution of higher-order boundary value problems in finite domains,” Abstract and Applied Analysis, vol. 2012, Art. no. 401217, 14 pp. (2011), doi: 10.1155/2012/401217.
[11] R. Hirota, “Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons,” Physical Review Letters, vol. 27, pp. 1192–1194 (1971).
[12] K. U. Tariq, M. Inc, and R. Javed, “On some novel soliton solutions to the generalized (3+1)-dimensional Boiti-Leon-Manna-Pempinelli model using two different approaches,” Revista Mexicana de Física, vol. 68, no. 5, pp. 051403-1–051403-16 (2022).
[13] Z. Qinghao and Q. Jianming, “On the exact solutions of nonlinear potential Yu-Toda-Sasa-Fukuyama equation by different methods,” Discrete Dynamics in Nature and Society (2022), doi: 10.1155/2022/2179375.
[14] C. Hanlin, X. Zhenhui, and D. Zhengde, “Rogue wave for the (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation,” Discrete Dynamics in Nature and Society (2014), doi: 10.1155/2014/378167.
[15] S. A. Mehdi, E. A. Kuffi, and J. A. Jasim, “Solving the partial differential equations by using SEJI integral transform,” Journal of Interdisciplinary Mathematics, vol. 26 (2023), doi: 10.47974/JIM-1611.
[16] M. S. Mechee and S. H. Aidi, “Some generalized numerical methods for solving higher-order fractional partial differential equations with application,” Journal of Interdisciplinary Mathematics, vol. 26, no. 7, pp. 1391–1400 (2023), doi: 10.47974/JIM-1556.

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