New solitary solutions for stochastic Kakutani–Matsuuchi model of internal gravity waves

Abeer H. Alblowy; Elsayed M. Elsayed; Wael W. Mohammed; Abeer H. Alblowy; Elsayed M. Elsayed; Wael W. Mohammed

doi:10.3934/math.2025716

AIMS Mathematics

2025, Volume 10, Issue 7: 15975-15990. doi: 10.3934/math.2025716

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New solitary solutions for stochastic Kakutani–Matsuuchi model of internal gravity waves

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 03 May 2025 Revised: 01 July 2025 Accepted: 04 July 2025 Published: 16 July 2025
MSC : 60H15, 60H10, 35Q51, 35A20

Here, we consider the stochastic Kakutani–Matsuuchi model (SKMM) perturbed by multiplicative noise in the Itô sense. This model describes the behavior of these waves as they propagate through a stratified fluid medium, such as the Earth's atmosphere or ocean. Internal gravity waves are generated by disturbances in the density or temperature of the fluid and can play a significant role in transporting energy and momentum throughout the system. By applying two different techniques, namely the extended tanh function method and the mapping method, we obtain new periodic soliton, dark soliton, bright soliton, anti-Kink soliton and Kink soliton solutions for SKMM. Because the Kakutani–Matsuuchi model is important in studying internal gravity waves in the atmosphere and oceans, the solutions of the SKMM are beneficial in understanding several fascinating scientific phenomena. Using MATLAB, we exhibit several 2D and 3D graphs that illustrate the impact of the noise on the solutions of SKMM.
- stochastic PDE,
- exact solutions,
- stability by noise,
- mapping method,
- extended tanh function method
Citation: Abeer H. Alblowy, Elsayed M. Elsayed, Wael W. Mohammed. New solitary solutions for stochastic Kakutani–Matsuuchi model of internal gravity waves[J]. AIMS Mathematics, 2025, 10(7): 15975-15990. doi: 10.3934/math.2025716

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Abstract

Here, we consider the stochastic Kakutani–Matsuuchi model (SKMM) perturbed by multiplicative noise in the Itô sense. This model describes the behavior of these waves as they propagate through a stratified fluid medium, such as the Earth's atmosphere or ocean. Internal gravity waves are generated by disturbances in the density or temperature of the fluid and can play a significant role in transporting energy and momentum throughout the system. By applying two different techniques, namely the extended tanh function method and the mapping method, we obtain new periodic soliton, dark soliton, bright soliton, anti-Kink soliton and Kink soliton solutions for SKMM. Because the Kakutani–Matsuuchi model is important in studying internal gravity waves in the atmosphere and oceans, the solutions of the SKMM are beneficial in understanding several fascinating scientific phenomena. Using MATLAB, we exhibit several 2D and 3D graphs that illustrate the impact of the noise on the solutions of SKMM.

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