Generalized invariant manifolds for integrable equations and their applications

In the article we discuss notion of generalized invariant manifold introduced in our previous study. literature method differential constraints is well known as a tool for constructing particular solutions nonlinear partial equations. Its essence adding to PDE, much simpler, rule ordinary, equation, compatible with given one. Then any solution ODE PDE well. However main problem find this ODE. Our generalization that look an ordinary equation not itself, but its linearization. Such effectively sought. Moreover, it allows one construct such important attributes integrability theory Lax pairs and recursion operators integrable paper, show they provide way