  We report on the dynamics of the spin-1/2 quasi-one-dimensional frustrated
magnet LiCuVO$\mathrm{_4}$ measured by nuclear spin relaxation in high magnetic
fields 10--34 T, in which the ground state has spin-density-wave order. The
spin fluctuations in the paramagnetic phase exhibit striking anisotropy with
respect to the magnetic field. The transverse excitation spectrum probed by
$^{51}$V nuclei has an excitation gap, which increases with field. On the other
hand, the gapless longitudinal fluctuations sensed by $^7$Li nuclei grow with
lowering temperature, but tend to be suppressed with increasing field. Such
anisotropic spin dynamics and its field dependence agree with the theoretical
predictions and are ascribed to the formation of bound magnon pairs, a
remarkable consequence of the frustration between ferromagnetic nearest
neighbor and antiferromagnetic next-nearest-neighbor interactions.
