THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Kang-Hua Yan

,

Xu-Wei Lu

,

Chang Liu

,

Wen-Min Li

BELL SHAPE SOLITARY, ANTI-KINK SOLITARY AND PERIODIC WAVE SOLUTIONS OF THE BENJAMIN ONO EQUATION FOR SHALLOW WATER WAVES

ABSTRACT
In this study, the Benjamin Ono equation which acts a key role for the shallow water waves is explored. Two effective approaches namely the Bernoulli sub-equation function method and simple frequency formulation method are adopted to extract some different wave solutions, which include the bell shape solitary, anti-kink solitary and periodic wave solutions. Correspondingly, the outlines of the diverse wave solutions are unveiled graphically through MAPLE.
KEYWORDS
Bernoulli sub-equation function method, Benjamin Ono equation, simple frequency formulation, solitary wave solutions
PAPER SUBMITTED: 2024-08-12
PAPER REVISED: 2024-09-14
PAPER ACCEPTED: 2024-12-06
PUBLISHED ONLINE: 2025-06-01
DOI REFERENCE: https://doi.org/10.2298/TSCI2502533Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2025, VOLUME 29, ISSUE Issue 2, PAGES [1533 - 1538]
REFERENCES
  1. Duran, S., An Investigation of the Physical Dynamics of a Traveling Wave Solution Called a Bright Soliton, Physica Scripta, 96 (2021), 12, ID125251
  2. Duran, S., et al., A Study on Solitary Wave Solutions for the Zoomeron Equation Supported by 2-D Dynamics, Physica Scripta, 98 (2023), 12, ID125265
  3. Seadawy, A. R., et al., Analytical Wave Solutions of the (2+1)-Dimensional Boiti-Leon-Pempinelli and Boiti-Leon-Manna-Pempinelli Equations by Mathematical Methods, Mathematical Methods in the Applied Sciences, 44 (2021), 18, pp. 14292-14315
  4. Seadawy, A. R., et al., Bifurcation Solitons, Y-type, Distinct Lumps and Generalized Breather in the Thermophoretic Motion Equation Via Graphene Sheets, Alexandria Engineering Journal, 87 (2024), Jan., pp. 374-388
  5. Liu, J. H., et al., On the Variational Principles of the Burgers-Korteweg-de Vries Equation in Fluid Mechanics, EPL, 149 (2025) 5, ID52001
  6. Hosseini, K., et al., New Optical Solitons of Cubic-Quartic Non-Linear Schrodinger Equation, Optik, 157 (2018), Mar., pp. 1101-1105
  7. Ma, W. X., A Novel Kind of Reduced Integrable Matrix mKdV Equations and Their Binary Darboux Transformations, Modern Physics Letters B, 36 (2022), 20, ID2250094
  8. Yang, D. Y., et al., Lax Pair, Darboux Transformation, Breathers and Rogue Waves of an N-Coupled Non-Autonomous Non-Linear Schrodinger System for an Optical Fiber or a Plasma, Non-Linear Dynamics, 107 (2022), 3, pp. 2657-2666
  9. Wang, K. J., et al., Phase Portrait, Bifurcation and Chaotic Analysis, Variational Principle, Hamiltonian, Novel Solitary and Periodic Wave Solutions of the New Extended Korteweg-De Vries-Type Equation, Mathematical Methods in the Applied Sciences, On-line first, doi.org/10.1002/mma.10852, 2025
  10. Liang, Y. H., et al., Diverse Wave Solutions to the New Extended (2+1)-Dimensional Non-Linear Evolution Equation: Phase Portrait, Bifurcation and Sensitivity Analysis, Chaotic Pattern, Variational Principle and Hamiltonian, International Journal of Geometric Methods in Modern Physics, 22 (2025), ID2550158
  11. Zayed, E. M. E., et al., Cubic-Quartic Solitons in Couplers with Optical Metamaterials Having Power Law of Refractive Index, Journal of Non-linear Optical Physics and Materials, 29 (2020), 3, ID 20500095
  12. Ozisik, M., et al., The Bell-Shaped Perturbed Dispersive Optical Solitons of Biswas-Arshed Equation Using the New Kudryashov's Approach, Optik, 267 (2022), ID169650
  13. Ma, Y. X., et al., Painleve Analysis, Backlund Transformations and Traveling-Wave Solutions for a (3+1)-Dimensional Generalized Kadomtsev-Petviashvili Equation in a Fluid, International Journal of Modern Physics B, 35 (2021), 7, ID2150108
  14. Yin, Y. H., et al., Bäcklund Transformation, Exact Solutions and Diverse Interaction Phenomena to a (3+1)-Dimensional Non-Linear Evolution Equation, Non-Linear Dynamics, 108 (2022), 4, pp. 4181-4194
  15. Muhammad, T., et al., Traveling Wave Solutions to the Boussinesq Equation Via Sardar Sub-Equation Technique, AIMS Mathematics, 7 (2022), 6, pp. 11134-11149
  16. Onder, I., et al., On the Optical Soliton Solutions of Kundu-Mukherjee-Naskar Equation via Two Different Analytical Methods, Optik, 257 (2022), ID168761
  17. Wang, K. J., et al., Lump Wave, Breather Wave and the other Abundant Wave Solutions to the (2+1)-Dimensional Sawada-Kotera-Kadomtsev Petviashvili Equation for Fluid Mechanic, Pramana, 99 (2025), 1, ID40
  18. Wang, K. J., et al., Novel Singular and Non-Singular Complexiton, Interaction Wave and the Complex Multi-Soliton Solutions to the Generalized Non-Linear Evolution Equation, Modern Physics Letters B, 39 (2025), ID2550135
  19. Zayed, E. M. E., et al., Cubic-Quartic Polarized Optical Solitons and Conservation Laws for Perturbed Fokas-Lenells Model, Journal of Non-linear Optical Physics and Materials, 30 (2021), 3, ID21500053
  20. Abdou, M. A., A Generalized Auxiliary Equation Method and Its Applications, Non-Linear Dynamics, 52 (2008), 1, pp. 95-102
  21. Alam, M. N., et al., Exact Traveling Wave Solutions of the KP-BBM Equation by Using the New Approach of Generalized (G′/G)-Expansion Method, SpringerPlus, 2 (2013), 1, pp. 1-7
  22. Teymuri Sindi, C., et al., Wave Solutions for Variants of the KdV-Burger and the K(N,N)-Burger Equations by the Generalized G′/G-Expansion Method, Mathematical Methods in the Applied Sciences, 40 (2017), 12, pp. 4350-4363
  23. Gkogkou, A., et al., Inverse Scattering Transform for the Complex Coupled Short-Pulse Equation, Studies in Applied Mathematics, 148 (2022), 2, pp. 918-963
  24. Wang, K. J, et al., Bifurcation Analysis, Chaotic Behaviors, Variational Principle, Hamiltonian and Diverse Optical Solitons of the Fractional Complex Ginzburg-Landau Model, International Journal of Theoretical Physics, On-line first: doi.org/10.1007/s10773-025-05977-9, 2025
  25. Raza, N., et al., Optical Dark and Dark-Singular Soliton Solutions of (1+2)-Dimensional Chiral Non-Linear Schrodinger's Equation, Waves in Random and Complex Media, 29 (2019), 3, pp. 496-508
  26. Aderyani, S. R., et al., The Exact Solutions of the Conformable Time-Fractional Modified Non-Linear Schrödinger Equation by the Trial Equation Method and Modified Trial Equation Method, Advances in Mathematical Physics, 2022 (2022), ID4318192
  27. Alquran, M., et al., New Topological and Non-Topological Unidirectional-Wave Solutions for the Modified-Mixed KdV Equation and Bidirectional-Waves Solutions for the Benjamin Ono Equation Using Recent Techniques, Journal of Ocean Engineering and Science, 7 (2022), 2, pp. 163-169
  28. Syam, M. I., The Solution of Cahn-Allen Equation Based on Bernoulli Sub-Equation Method, Results in Physics, 14 (2019), ID102413
  29. He, J.-H., The Simplest Approach to Non-Linear Oscillators, Results in Physics, 15 (2019), ID102546
PDF VERSION [DOWNLOAD]
Bell shape solitary, anti-kink solitary and periodic wave solutions of the Benjamin Ono equation for shallow water waves

2025 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence