Cnoidal Waves, Solitary Waves, Shock Waves and Conservation Laws of the Generalized Cubic Boussinesq-Type Model for Shallow Water Wave Dynamics

Authors

  • Anjan Biswas Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245–2715, USA. https://orcid.org/0000-0002-8131-6044
  • Ming-Yue Wang Key Laboratory of Mechanics on Disaster and Environment in Western China, The Ministry of Education, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, 730000, China
  • Abdul H. Kara School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits, 2050, Johannesburg, South Africa
  • Yakup Yildirim Department of Computer Engineering, Biruni University, Istanbul, 34010, Turkey
  • Luminita Moraru Department of Chemistry, Physics and Environment, Faculty of Sciences and Environment, Dunarea de Jos University of Galati, 47 Domneasca Street, 800008, Romania
  • Carmelia M. Balanica Department of Applied Sciences, Cross-Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati, 800201, Romania
  • Layth Hussein Department of Computers Techniques Engineering, College of Technical Engineering, The Islamic University, Najaf, Iraq
  • Anwar Ja’far Mohamad Jawad Department of Computer Technical Engineering, Al-Rafidain University College, Baghdad, 10064, Iraq

DOI:

https://doi.org/10.37256/cm.6220256389

Keywords:

solitary waves, shallow water, Boussinesq, conservation laws

Abstract

The paper addresses the latest form of Boussinesq equation with generalized form of cubic nonlinearity. The solitary waves are recovered from the model using traveling wave hypothesis. The conservation laws are recovered from the model. The conservation laws are obtained using the method of multipliers. Finally, the complete discriminant method yields shock waves and cnoidal waves as well. The numerical simulations supplement the analytical results.

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Published

2025-03-19

How to Cite

1.
Biswas A, Wang M-Y, Kara AH, Yildirim Y, Moraru L, Balanica CM, Hussein L, Jawad AJM. Cnoidal Waves, Solitary Waves, Shock Waves and Conservation Laws of the Generalized Cubic Boussinesq-Type Model for Shallow Water Wave Dynamics. Contemp. Math. [Internet]. 2025 Mar. 19 [cited 2025 Apr. 2];6(2):1973-87. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/6389

Issue

Contemporary Mathematics, Volume 6 Issue 2 (2025)

Section

Research Article

License

Copyright (c) 2025 Anjan Biswas, Ming-Yue Wang, Abdul H. Kara, Yakup Yildirim, Luminita Moraru, Carmelia M. Balanica, Layth Hussein, Anwar Ja’far Mohamad Jawad

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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