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

Abstract

In the following paper, we investigate nonlinear Rossby-Khantadze waves, by taking into account inhomogeneity in the geomagnetic field and angular velocity - due to Earth's differential rotation. Considering the system to be weakly nonlinear, we make use of perturbation theory to derive a new (2+1)-D generalized form of Boussineq equation. We evaluate the obtained equation by using the qualitative theory of ordinary differential equations (ODEs), and bifurcation theory of dynamical systems. The obtained numerical results show that the aforementioned solutions of the traveling waves correspond to Rossby-Khantadze solitons.