Effect of the free parameters on the Biswas-Arshed model with a unified technique

Islam, Shamsul; Bashar, Md. Habibul; Arafat, S. M. Yiasir; Wang, Hanfeng; Roshid, Harun-Or

doi:10.1016/j.cjph.2022.04.022

Cited by 15 publications

(1 citation statement)

References 29 publications

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“…In this paper, we have applied the GUM [19] to derive exact solutions for the DSS. The GUM is an enhanced version of the unified method [20,21] that many authors [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] have successfully applied to solve different types of NPDEs. Compared with other methods, the GUM requires less computational work with high reliability to solve NPDEs.…”

Section: Introductionmentioning

confidence: 99%

New Exact Solutions of the Drinfeld-Sokolov System by the Generalized Unified Method

AYDEMİR

2023

Journal of New Theory

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In this study, we apply the generalized unified method (GUM), an enhanced version of the unified method, to find novel exact solutions of the Drinfeld-Sokolov System (DSS) that models the dispersive water waves in fluid dynamics. Moreover, 3D and 2D graphs of some of the obtained exact solutions are plotted to present how various characteristic forms they have. The results show that the presented method simplifies the computation process on the computer in a highly reliable and straightforward manner while providing the solutions in more general forms. In addition, the GUM has great potential to apply to a wide range of problems, including nonlinear partial differential equations (NPDEs) and fractional partial differential equations (FPDEs) for finding exact solutions.

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Section: Introductionmentioning

confidence: 99%

New Exact Solutions of the Drinfeld-Sokolov System by the Generalized Unified Method

AYDEMİR

2023

Journal of New Theory

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Sensitivity and wave propagation analysis of the time-fractional (3+1)-dimensional shallow water waves model

Şenol,

Gençyiğit,

Demirbilek

et al. 2024

Z. Angew. Math. Phys.

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This study investigates the exact solutions of the time-fractional (3+1)-dimensional combined Korteweg–de Vries Benjamin–Bona–Mahony (KdV-BBM) equation. The considered model describes the long surface gravity waves of small amplitude, which portrays the two-way propagation of waves. The modified generalized Kudryashov method and the exp(-$$\varphi (\xi $$ φ ( ξ ))-expansion methods are employed to resolve the aforementioned issue because of their effectiveness and simplicity. For generality, the time fractional version is studied; more advanced solutions that do not exist in the literature were obtained. As a result, a variety of the exact wave solutions of the conformable (3+1)-dimensional KdV-BBM equation are obtained. The dynamical behaviors of some obtained solutions are represented with the proper parameter values. The used methods yield noteworthy results in obtaining the analytical solutions of fractional differential equations under various conditions. Besides, the sensitivity of regarding dynamical system is assessed to show the numerical stability effects.

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Application of the generalized unified method to solve (2+1)-dimensional Kundu–Mukherjee–Naskar equation

Aydemir

2023

Opt Quant Electron

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Effect of the free parameters on the Biswas-Arshed model with a unified technique

Cited by 15 publications

References 29 publications

New Exact Solutions of the Drinfeld-Sokolov System by the Generalized Unified Method

New Exact Solutions of the Drinfeld-Sokolov System by the Generalized Unified Method

Sensitivity and wave propagation analysis of the time-fractional (3+1)-dimensional shallow water waves model

Application of the generalized unified method to solve (2+1)-dimensional Kundu–Mukherjee–Naskar equation

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