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A similar argument can be made for Hall-MHD solitons in which the acceleration of the protons is 0(VAp), the length scale is VA/p yielding the fractional charge sep- aration n/n  2 /! 2 =V 2 A /c 2 , where VA andp are the Alfven speed based on the proton mass density and the pro- ton gyrofrequency, respectively, demanding that n/n is rel- ativistically small and divE6=0. This is the reason why the standard Hall-MHD equations do not require Poisson's equa- tion and do not impose any constraint on divE. The electric fields are derived from Faraday's law and the equations of the motion together with the condition divj=0. Poisson's equation provides us only with an estimate of the charge sep- aration ratio n/n as was shown above. In the classic nonlinear wave propagating transverse to the

nonlinear processes in geophysics

Comment on &amp;quot;Obliquely propagating large amplitude solitary waves in charge neutral plasmas&amp;quot; by F. Verheest, Nonlin. Processes Geophys., 14, 49–57, 2007