The effect of including the electron temperature gradient and higher‐order terms in the expansion of the density profile in the equations for nonlinear drift waves in plasmas is studied, as well as the effect of expanding the equation for nonlinear Rossby waves to higher orders in the amplitude. The two cases are very similar, and earlier studies have concluded that these effects would make a new kind of stationary monopole vortex solution possible. This solution would have a unique functional form in the whole plane, and for some parameter values no closed streamlines. It is shown that this conclusion is correct, and that such solutions do not exist. It is also pointed out that these additional effects become particularly important in the region of very long wavelengths, where they give rise to wave breaking and a transfer of energy toward shorter wavelengths. This can prevent the condensation to zonal flows that has been predicted earlier.