  The constraints for evolution equations with some special form of Lax pair
are first investigated. We show by examples how the method is rooted in the
classical literatures and how the ignored constraints provide nontrivial
solutions. Then we showed, by the example of the KdV, how this special form of
Lax pair may be found by the method of EW. At last we propose how constraints
should be imposed for general Lax pairs including nonlinear ones, with which
the true Lax pairs and the fake ones can be distinguished easily. The linearity
nature in integrable partial differential equations seems to have been
revealed.
