  The extended Gutzwiller trajectory approach is presented for the
semiclassical description of nuclear collective dynamics, in line with the main
topics of the fruitful activity of V.G. Solovjov. Within the Fermi-liquid
droplet model, the leptodermous effective surface approximation was applied to
calculations of energies, sum rules and transition densities for the
neutron-proton asymmetry of the isovector giant-dipole resonance and found to
be in good agreement with the experimental data. By using the Strutinsky shell
correction method, the semiclassical collective transport coefficients such as
nuclear inertia, friction, stiffness, and moments of inertia can be derived
beyond the quantum perturbation approximation of the response function theory
and the cranking model.The averaged particle-number dependence of the low-lying
collective vibrational states are described in good agreement with basic
experimental data, mainly due to an enhancement of the collective inertia as
compared to its irrotational flow value. Shell components of the moment of
inertia are derived in terms of the periodic-orbit free-energy shell
corrections. A good agreement between the semiclassical extended Thomas-Fermi
moments of inertia with shell corrections and the quantum results is obtained
for different nuclear deformations and particle numbers. Shell effects are
shown to be exponentially dampted out with increasing temperature in all the
transport coefficients.
