## THERMAL SCIENCE

International Scientific Journal

### ANALYTICAL AND SEMI ANALYTICAL SOLUTIONS OF THE INTERNAL WAVES OF DEEP-STRATIFIED FLUIDS

**ABSTRACT**

In this paper, we study the soliton wave of the fractional Benjamin-Ono equation based on the extended simplest equation method. The accuracy of the obtained soliton wave solutions is investigated by comparing the obtained analytical and semi-analytical solutions. The semi-analytical solutions are constructed by applying the Adomian decomposition method. The semi-analytical method is used based on the constructed initial and boundary conditions from the obtained analytical solutions. Both solutions (analytical and semi-analytical) are plotted through different techniques for explaining the internal waves of deep-stratified fluids.

**KEYWORDS**

PAPER SUBMITTED: 2021-03-05

PAPER REVISED: 2021-03-20

PAPER ACCEPTED: 2021-04-17

PUBLISHED ONLINE: 2021-12-18

- Khater, M. M. A., et al., Abundant New Computational Wave Solutions of the GM-DP-CH Equation Via Two Modified Recent Computational Schemes, Journal of Taibah University for Science, 14 (2020), 1, pp. 1554-1562
- Khater, M. M. A., et al., Effective Computational Schemes for a Mathematical Model of Relativistic Electrons Arising in the Laser Thermonuclear Fusion, Results in Physics, 19 (2020), Dec., ID 103701
- Khater, M. M. A., et al., Abundant Stable Computational Solutions of Atangana-Baleanu Fractional Nonlinear HIV-1 Infection of CD4+ T-Cells of Immunodeficiency Syndrome, Results in Physics, 22 (2021), Mar., ID 103890
- Khater, M. M. A., Behzad, G., On the Solitary Wave Solutions and Physical Characterization of Gas Diffusion in a Homogeneous Medium Via Some Efficient Techniques, The European Physical Journal Plus, 136 (2021), 4, pp. 1-28
- Khater, M. M. A., et al., Diverse Accurate Computational Solutions of the Non-Linear Klein-Fock-Gordon Equation, Results in Physics, 23 (2021), Apr., ID 104003
- Khater, M. M. A., et al., Novel Computational and Accurate Numerical Solutions of the Modified Benja-min-Bona-Mahony (BBM) Equation Arising in the Optical Illusions Field, Alexandria Engineering Jour-nal, 60 (2021), 1, pp. 1797-1806
- Khater, M. M. A., et al., Computational Simulation for the (1+1)-Dimensional Ito Equation Arising Quan-tum Mechanics and Non-linear Optics, Results in Physics, 19 (2020), Dec., ID 103572
- Khater, M. M. A., et al., Optical Soliton Structure of the Sub-10-Fs-Pulse Propagation Model, Journal of Optics, 50 (2021), 1, pp. 109-119
- Zheng, H., et al., Travelling Wave Solutions of the General Regularized Long Wave Equation, Qualitative Theory of Dynamical Systems, 20 (2021), 1, pp. 1-21
- Singh, M., Generalized Symmetries and Conservation Laws of (3+1)-Dimensional Variable Coefficient Zakharov-Kuznetsov Equation, Computational Methods for Differential Equations, 9 (2021), 1, pp. 300-312
- Khater, M. M. A., et al., Multi-Solitons, Lumps, and Breath Solutions of the Water Wave Propagation with Surface Tension Via Four Recent Computational Schemes, Ain Shams Engineering Journal, 12 (2021), 3, pp. 3031-3041
- Khater, M. M. A., On the Dynamics of Strong Langmuir Turbulence Through the five Recent Numerical Schemes in the Plasma Physics, Numerical Methods for Partial Differential Equations, On-line first, doi.org/10.1002/num.22681, 2020
- Attia, R. A. M., et al., Computational and Numerical Simulations for the Deoxyribonucleic Acid (DNA) Model, Discrete & Continuous Dynamical Systems-S, 14 (2021), 10, pp. 3459-3478
- Khater, M. M. A., et al., Computational Simulation for the (1+ )-Dimensional Ito Equation Arising Quan-tum Mechanics and Non-Linear Optics, Results in Physics, 19 (2020), ID 103572
- Khater, M. M. A., et al., Computational and Approximate Solutions of Complex Non-Linear Fokas-Le-nells Equation Arising in Optical Fiber, Results in Physics, 25 (2021), June, ID 104322
- Khater, M. M. A., et al., Diverse Accurate Computational Solutions of the Non-Linear Klein-Fock-Gordon Equation, Results in Physics, 23 (2021), Apr., ID 104003
- Khater, M. M. A., et al., Analytical and Semi‐Analytical Solutions for Time‐Fractional Cahn-Allen Equa-tion, Mathematical Methods in the Applied Sciences, 44 (2021), 3, ID 2682-2691
- Khater, M. M. A., Behzad, G., On the Solitary Wave Solutions and Physical Characterization of Gas Dif-fusion in a Homogeneous Medium Via Some Efficient Techniques, The European Physical Journal Plus, 136 (2021), 4, pp. 1-28
- Khater, M. M. A., Diverse Solitary and Jacobian Solutions in a Continually Laminated Fluid with Respect to Shear Flows Through the Ostrovsky Equation, Modern Physics, Letters B, 35 (2021), 13, ID 2150220
- Wu, Li, et al., Computational Schemes Between The Exact, Analytical and Numerical Solution in Present of Time-Fractional Ecological Model, Physica Scripta, 96 (2020), 3, ID 035207
- Khater, M. M. A., et al., On the Interaction Between (Low & High) Frequency of (Ion-Acoustic & Lang-muir) Waves in Plasma Via Some Recent Computational Schemes, Results in Physics, 19 (2020), Dec., ID 103684
- Fokas, A. S., Fuchssteiner, B., The Hierarchy of the Benjamin-Ono Equation, Physics, Letters A, 86 (1981), 6-7, pp. 341-345
- Sun, R., Complete Integrability of the Benjamin-Ono Equation on the Multi-Soliton Manifolds, Commu-nications in Mathematical Physics, 383 (2021), 2, pp. 1051-1092
- Grimshaw, R. H. J., et al., Interaction of Internal Solitary Waves with Long Periodic Waves Within the Rotation Modified Benjamin-Ono Equation, Physica D: Non-Linear Phenomena, 419 (2021), May, ID 132867