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

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.