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The mBBM equation: a mathematical key to unlocking wave behavior in fluids

Raghda Attia Mahmoud Attia

Raghda Attia Mahmoud Attia

School of Medical Informatics and Engineering, Xuzhou Medical UniversityXuzhou, China
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Mahmoud Attia, Raghda Attia
 and 
Mostafa Mohamed Abdelazeem Khater

Mostafa Mohamed Abdelazeem Khater

  • School of Medical Informatics and Engineering, Xuzhou Medical UniversityXuzhou, China
  • Institute of Digital Economy, Ugra State UniversityKhanty-Mansiysk, Russia
  • Department of Basic Sciences, High Institute for Engineering and Technology Al ObourCairo, Egypt
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Abdelazeem Khater, Mostafa Mohamed
  
Sep 20, 2024
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Article Category: Original Study
Published Online: Sep 20, 2024
Page range: 171 - 184
Received: Oct 11, 2023
Accepted: Mar 31, 2024
DOI: https://doi.org/10.2478/ijmce-2025-0014
Keywords
© 2025 Raghda Attia Mahmoud Attia et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Analytical solitary wave solutions of the mBBM equation represented through diverse graphical techniques via 3D, 2D and contour plots for equations (11), (13), (15).
Analytical solitary wave solutions of the mBBM equation represented through diverse graphical techniques via 3D, 2D and contour plots for equations (11), (13), (15).

Fig. 2

Quantitative validation of analytical solutions against numerical solutions through absolute error analysis. (a–c) Absolute error between solutions obtained via the EAE method and the ECBS numerical method at defined intervals. (d–f) Absolute error comparison between solutions derived from the IKud method and ECBS numerical solutions at specified intervals.
Quantitative validation of analytical solutions against numerical solutions through absolute error analysis. (a–c) Absolute error between solutions obtained via the EAE method and the ECBS numerical method at defined intervals. (d–f) Absolute error comparison between solutions derived from the IKud method and ECBS numerical solutions at specified intervals.

Fig. 3

Comparative assessment of solution accuracy for the IKud and EAE analytical techniques, benchmarked against ECBS numerical solutions.
Comparative assessment of solution accuracy for the IKud and EAE analytical techniques, benchmarked against ECBS numerical solutions.

Fig. 4

Stream plot illustrating the propagation of solitary wave solutions in the mBBM model.
Stream plot illustrating the propagation of solitary wave solutions in the mBBM model.

Fig. 5

Comparative stream plots demonstrating the influence of parameter modifications on the propagation behavior of solitary waves in the mBBM model.
Comparative stream plots demonstrating the influence of parameter modifications on the propagation behavior of solitary waves in the mBBM model.

Quantitative assessment of solution accuracy_

Value of ℨ Analytical solution Numerical solution Absolute Error
0 0 0 0
0.001 9.99999666666800E-04 9.99979867286439E-04 1.97993803609242E-08
0.002 1.99999733333760E-03 1.99995893459001E-03 3.83987475887151E-08
0.003 2.99999100003240E-03 2.99993640193329E-03 5.45980991108024E-08
0.004 3.99997866680320E-03 3.99991146934972E-03 6.71974534757411E-08
0.005 4.99995833375000E-03 4.99988333688908E-03 7.49968609116067E-08
0.006 5.99992800103679E-03 5.99985120462290E-03 7.67964138817870E-08
0.007 6.99988566890756E-03 6.99981427264991E-03 7.13962576490146E-08
0.008 7.99982933770229E-03 7.99977174110146E-03 5.75966008307255E-08
0.009 8.99975700787294E-03 8.99972281014699E-03 3.41977259531168E-08
0.01 9.99966667999946E-03 9.99966667999946E-03 0
Language:
English
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