  We use recently proposed four-spin bond-operator technique (BOT) to discuss
spectral properties of frustrated spin-$\frac12$ $J_1$--$J_2$ Heisenberg
antiferromagnet on square lattice at $J_2<0.4J_1$ (i.e., in the N\'eel ordered
phase). This formalism is convenient for the consideration of low-lying
excitations which appear in conventional approaches as multi-magnon bound
states (e.g., the Higgs excitation) because separate bosons describe them in
BOT. At $J_2=0$, the obtained magnon spectrum describes accurately available
experimental data. However, calculated one-magnon spectral weights and the
transverse dynamical structure factor (DSF) do not reproduce experimental
findings quantitatively around the momentum ${\bf k}=(\pi,0)$. Then, we do not
support the conjecture that the continuum of excitations observed
experimentally and numerically near ${\bf k}=(\pi,0)$ is of the Higgs-magnon
origin. Upon $J_2$ increasing, one-magnon spectral weights decrease and spectra
of high-energy spin-0 and spin-1 excitations move down. One of spin-0
quasiparticles becomes long-lived and its spectrum merges with the magnon
spectrum in the most part of the Brillouin zone at $J_2\approx0.3J_1$. We
predict that the Higgs excitation and another spin-0 quasiparticle become
long-lived around ${\bf k}=(\pi/2,\pi/2)$ at $J_2\agt0.3J_1$ and produce sharp
anomalies in the longitudinal DSF.
