  Recent results on solutions to the equation of motion of the cubic fermionic
string field theory and an equivalence of non-polynomial and cubic string field
theories are discussed. To have a possibility to deal with both GSO(+) and
GSO(-) sectors in the uniform way a matrix formulation for the NS fermionic SFT
is used. In constructions of analytical solutions to open string field theories
truncated pure gauge configurations parameterized by wedge states play an
essential role. The matrix form of this parametrization for the NS fermionic
SFT is presented. Using the cubic open superstring field theory as an example
we demonstrate explicitly that for the large parameter of the perturbation
expansion these truncated pure gauge configurations give divergent
contributions to the equation of motion on the subspace of the wedge states.
The perturbation expansion is cured by adding extra terms that are nothing but
the terms necessary for the equation of motion contracted with the solution
itself to be satisfied.
