RESUMEN
We have applied the Painleve
criterion to the supersymmetric nonlinear Schrödinger equation. This particular
system of fermionic and bosonic field shows up a rich spectrum of resonances
and it can be explicitly proved that the expansion coefficients at the
resonance positions can remain arbitrary. At this point it is worth noting that
even when the extra nonlinear field (which is fermionic in this case) is
considered to be bosonic, the resulting system turns out to satisfy the
Painleve test so that this second system may be thought of as a new completely
integrable system whose Lax pair is still to be found.