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