  Stationary solutions on a bounded interval for an initial-boundary value
problem to Korteweg--de~Vries and modified Korteweg--de~Vries equation (for the
last one both in focusing and defocusing cases) are constructed. The method of
the study is based on the theory of conservative systems with one degree of
freedom. The obtained solutions turn out to be periodic. Exact relations
between the length of the interval and coefficients of the equations which are
necessary and sufficient for existence of nontrivial solutions are established.
