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The constraints for evolution equations with some special form of Lax pairare first investigated. We show by examples how the method is rooted in theclassical literatures and how the ignored constraints provide nontrivialsolutions. Then we showed, by the example of the KdV, how this special form ofLax pair may be found by the method of EW. At last we propose how constraintsshould be imposed for general Lax pairs including nonlinear ones, with whichthe true Lax pairs and the fake ones can be distinguished easily. The linearitynature in integrable partial differential equations seems to have beenrevealed.

Constraints for Evolution Equations with Some Special Form of Lax Pairs and Distinguishing Lax Pairs by Available Constraints