Modified KdV equation for magnetized Rossby waves in a zonal flow of the ionospheric E-layer

Nonlinear interaction of magnetized Rossby waves with sheared zonal flow in the Earth's ionospheric E-layer is investigated. It is shown that in case of weak nonlinearity 2D Charney vorticity equation can be reduced to the one-dimensional modified KdV equation. •Nonlinear interaction of magnetized Rossby waves with sheared zonal flow in the Earth's ionospheric E-layer is investigated.•In case of weak nonlinearity 2D Charney equation can be reduced to 1D modified KdV equation.•To find the asymptotic solution multiple scale method is used.