  Solutions and their evolutions of the quark gap equation are studied within
the Nambu-Jona--Lasinio model, which is a basic issue for studying the QCD
phase structure and locating the possible critical end point. It is shown that
in the chiral limit case of the vacuum, chiral symmetry will hold if the
coupling strength $G$ is small, then the system only has the Wigner solution at
$M=0$. If increasing $G$, two symmetric minima will appear as the positive and
`negative' Nambu solutions, however, the solution $M=0$ now corresponds to a
maximum instead of a minimum of the thermodynamical potential, so is not a
physically stable state anymore (we call it `pseudo-Wigner solution'). Besides,
it is shown that as the current quark mass $m$ increases, the pseudo-Wigner
solution will become negative, and disappear together with the negative Nambu
solution if $m$ is large enough. Similar things happen if we increase the
temperature or quark chemical potential $\mu$. Some interesting phenomenon is,
from some $\mu$ a second local minimum will show up. As $\mu$ increases
gradually, it will be stabler than the Nambu solution, survives even the Nambu
solution disappears, and approaches $m$, which are just the features of the
Wigner solution we expect.
