  We introduce GBDT version of Darboux transformation for symplectic and
Hamiltonian systems as well as for Shin-Zettl systems and Sturm-Liouville
equations. These are the first results on Darboux transformation for
general-type Hamiltonian and for Shin-Zettl systems. The obtained results are
applied to the corresponding transformations of the Weyl-Titchmarsh functions
and to the construction of explicit solutions of dynamical symplectic systems,
of two-way diffusion equations and of indefinite Sturm-Liouville equations. The
energy of the explicit solutions of dynamical systems is expressed (in a quite
simple form) in terms of the parameter matrices of GBDT.
