  In previous work on Schwinger pair creation in purely time-dependent fields,
it was shown how to construct ``solitonic'' electric fields that do not create
scalar pairs with an arbitrary fixed momentum. We show that this construction
can be adapted to the fermionic case in two inequivalent ways, both closely
related to supersymmetric quantum mechanics for reflectionless potentials, and
both leading to the vanishing of the density of created pairs at certain values
of the P\"oschl-Teller like index $p$ of the associated Schr\"odinger equation.
For one of them, we are able to demonstrate that the pair non-creation can be
interpreted as a quantum interference effect using the phase-integral
formalism. Asymptotically for large $p$, here scalar particles are not created
for integer $p$ and fermions are not created for half integer $p$. Thus for any
given momentum we can construct electric fields that create scalar particles
but not spinor particles, and vice versa. In the scalar QED case, the solitonic
fields had originally been found using the Gelfand-Dikii equation, which is
related to the resolvent of the mode equation, and through it to the
(generalized) KdV equation [38]. This motivates us to develop for the spinor
QED case, too, an evolution equation that can be considered as a fermionic
generalization of the Gelfand-Dikii equation.
