  [Background] Giant resonance (GR) is a typical collective mode of vibration.
The deformation splitting of the isovector (IV) giant dipole resonance is well
established. However, the splitting of GRs with other multipolarities is not
well understood. [Purpose] I explore the IV monopole and quadrupole excitations
and attempt to obtain the generic features of IV giant resonances in deformed
nuclei by investigating the neutral and charge-exchange channels
simultaneously. [Method] I employ a nuclear energy-density functional (EDF)
method: the Skyrme-Kohn-Sham-Bogoliubov and the quasiparticle random-phase
approximation are used to describe the ground state and the transition to
excited states. [Results] I find the concentration of the monopole strengths in
the energy region of the isobaric analog or Gamow-Teller resonance irrespective
of nuclear deformation, and the appearance of a high-energy giant resonance
composed of the particle-hole configurations of $2\hbar \omega_0$ excitation.
Splitting of the distribution of the strength occurs in the giant monopole and
quadrupole resonances due to deformation. The lower $K$ states of quadrupole
resonances appear lower in energy and possess the enhanced strengths in the
prolate configuration, and vice versa in the oblate configuration, while the
energy ordering depending on $K$ is not clear for the $J=1$ and $J=2$
spin-quadrupole resonances. [Conclusions] The deformation splitting occurs
generously in the giant monopole and quadrupole resonances. The $K$-dependence
of the quadrupole transition strengths is largely understood by the anisotropy
of density distribution.
