  An important representation of the general-type fundamental solutions of the
canonical systems corresponding to matrix string equations is established using
linear similarity of a certain class of Volterra operators to the squared
integration. Explicit fundamental solutions of these canonical systems are also
constructed via the GBDT version of Darboux transformation. Examples and
applications to dynamical canonical systems are given. Explicit solutions of
the dynamical canonical systems are constructed as well. Three appendices are
dedicated to the Weyl--Titchmarsh theory for canonical systems, transformation
of a subclass of canonical systems into matrix string equations (and of a
smaller subclass of canonical systems into matrix Schr\"odinger equations), and
a linear similarity problem for Volterra operators.
