  We discuss spin-1/2 one-dimensional (1D) and quasi-1D magnets with competing
ferromagnetic nearest-neighbor $J_1$ and antiferromagnetic
next-nearest-neighbor $J$ exchange interactions in strong magnetic field $H$.
It is well known that due to attraction between magnons quantum phase
transitions (QPTs) take place at $H=H_s$ from the fully polarized phase to
nematic ones if $J>|J_1|/4$. Such a transition at $J>0.368|J_1|$ is
characterized by softening of the two-magnon bound-state spectrum. Using a bond
operator formalism we propose a bosonic representation of the spin Hamiltonian
containing, aside from bosons describing one-magnon spin-1 excitations, a boson
describing spin-2 excitations which spectrum coincides at $H\ge H_s$ with the
two-magnon bound-state spectrum obtained before. The presence of the bosonic
mode in the theory that softens at $H=H_s$ makes substantially standard the QPT
consideration. In 1D case at $H<H_s$, we find an expression for the
magnetization which describes well existing numerical data. Expressions for
spin correlators are obtained which coincide with those derived before either
in the limiting case of $J\gg|J_1|$ or using a phenomenological theory. In
quasi-1D magnets, we find that the boundary in the $H$--$T$ plane between the
fully polarized and the nematic phases is given by $H_s(0)-H_s(T)\propto
T^{3/2}$. Simple expressions are obtained in the nematic phase for static spin
correlators, spectra of magnons and the soft mode, magnetization and the
nematic order parameter. All static two-spin correlation functions are short
ranged with the correlation length proportional to $1/\ln(1+|J_1|/J)$.
Dynamical spin susceptibilities are discussed and it is shown that the soft
mode can be observed experimentally in the longitudinal channel.
