Preprints
https://doi.org/10.5194/egusphere-2025-123
https://doi.org/10.5194/egusphere-2025-123
28 Jan 2025
 | 28 Jan 2025
Status: this preprint is open for discussion and under review for Annales Geophysicae (ANGEO).

A Nonlinear Generalized Boussinesq Equation ((2+1)-D) for Rossby-Khantadze Waves

Laila Zafar Kahlon, Tamaz David Kaladze, Hassan Amir Shah, Taimoor Zaka, and Syed Assad Ul Azeem Bukhari

Abstract. In the following paper, we investigate nonlinear Rossby-Khantadze waves at a higher dimension, by taking the inhomogenities in the geomagnetic field and in angular velocity into account. Considering the system to be weakly nonlinear, we make use of perturbation theory to derive a new (2+1)–D general form of Boussineq equation, derived from the equation of potential vorticity. We evaluate the obtained equation by using the qualitative theory of ODEs, and bifurcation theory of dynamical systems. Through which we obtain the exact solution of the system in a co-moving frame of reference and for more information, we make use of dynamical analysis. Furthermore, we provide the exact numerical solutions. These results show that the aforementioned solutions of the traveling waves corresponds to Rossby-Khantadze solitons.

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Laila Zafar Kahlon, Tamaz David Kaladze, Hassan Amir Shah, Taimoor Zaka, and Syed Assad Ul Azeem Bukhari

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Laila Zafar Kahlon, Tamaz David Kaladze, Hassan Amir Shah, Taimoor Zaka, and Syed Assad Ul Azeem Bukhari
Laila Zafar Kahlon, Tamaz David Kaladze, Hassan Amir Shah, Taimoor Zaka, and Syed Assad Ul Azeem Bukhari

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Short summary
In this work, the investigation of Rossby-Khantadze waves with sheared zonal flows in E-ionosphere is presented. The spatially inhomogeneous Earth’s angular velocity and background magnetic field are considered. The field inhomogeneity makes the coupling of Rossby and Khantadze waves. The numerical work of obtained linear frequencies is done. By using the method of multiple scale, we obtained a new Boussinesq nonlinear equation. Also, we obtain the travelling solitary structures.
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