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[Background] Giant resonance (GR) is a typical collective mode of vibration.The deformation splitting of the isovector (IV) giant dipole resonance is wellestablished. However, the splitting of GRs with other multipolarities is notwell understood. [Purpose] I explore the IV monopole and quadrupole excitationsand attempt to obtain the generic features of IV giant resonances in deformednuclei by investigating the neutral and charge-exchange channelssimultaneously. [Method] I employ a nuclear energy-density functional (EDF)method: the Skyrme-Kohn-Sham-Bogoliubov and the quasiparticle random-phaseapproximation are used to describe the ground state and the transition toexcited states. [Results] I find the concentration of the monopole strengths inthe energy region of the isobaric analog or Gamow-Teller resonance irrespectiveof nuclear deformation, and the appearance of a high-energy giant resonancecomposed of the particle-hole configurations of $2\hbar \omega_0$ excitation.Splitting of the distribution of the strength occurs in the giant monopole andquadrupole resonances due to deformation. The lower $K$ states of quadrupoleresonances appear lower in energy and possess the enhanced strengths in theprolate configuration, and vice versa in the oblate configuration, while theenergy ordering depending on $K$ is not clear for the $J=1$ and $J=2$spin-quadrupole resonances. [Conclusions] The deformation splitting occursgenerously in the giant monopole and quadrupole resonances. The $K$-dependenceof the quadrupole transition strengths is largely understood by the anisotropyof density distribution.

Isovector giant monopole and quadrupole resonances in a Skyrme energy density functional approach with axial symmetry