In general, you can always decompose electric potentials due to the principle of superposition. However, in the case of the Suzen-Huang model it was done in order to separate the influence of an external electric field from the E-field that is created by the plasma itself (i.e. by the plasma density distribution). This yields two differential equations instead of one but these two equations can be solved easier as if you would treat both fields unseparated with just one equation.