On positive infinitely smooth vortex in zonal flow

Long waves propagating in a zonal flow within a layer of rotating liquid or atmosphere are considered in the paper. The theorem about non-trivial solutions of quasi-linear elliptical equations in $H^1(\mathbf R^n)$ is used. The existence of positive exponentially local vortex running along a geographic parallel is shown. The vortex has infinite smoothness. An example of the vortex has been calculated numerically.