  A notion of the generalized invariant manifold for a nonlinear integrable
lattice is considered. Earlier it has been observed that this kind objects
provide an effective tool for evaluating the recursion operators and Lax pairs.
In this article we show with an example of the Volterra chain that the
generalized invariant manifold can be used for constructing exact particular
solutions as well. To this end we first find an invariant manifold depending on
two constant parameters. Then we assume that ordinary difference equation
defining the generalized invariant manifold has a solution polynomially
depending on one of the spectral parameters and derive ordinary difference and
differential equations, for the roots of the polynomials. Efficiency of the
method is approved by some illustrative examples.
