  Magnetars are the most promising progenitors of Fast Radio Bursts (FRBs).
Strong radio waves propagating through the magnetar wind are subject to
non-linear effects, including modulation/filamentation instabilities. We derive
the dispersion relation for modulations of strong waves propagating in
magnetically-dominated pair plasmas focusing on dimensionless strength
parameters $a_0\lesssim 1$, and discuss implications for FRBs. As an effect of
the instability, the FRB radiation intensity develops sheets perpendicular to
the direction of the wind magnetic field. When the FRB front expands outside
the radius where the instability ends, the radiation sheets are scattered due
to diffraction. The FRB scattering timescale depends on the properties of the
magnetar wind. In a cold wind, the typical scattering timescale is $\tau_{\rm
sc}\sim{\rm\; \mu s-ms}$ at the frequency $\nu\sim 1{\rm\; GHz}$. The
scattering timescale increases at low frequencies, with the scaling $\tau_{\rm
sc}\propto\nu^{-2}$. The frequency-dependent broadening of the brightest pulse
of FRB 181112 is consistent with this scaling. From the scattering timescale of
the pulse, one can estimate that the wind Lorentz factor is larger than a few
tens. In a warm wind, the scattering timescale can approach $\tau_{\rm
sc}\sim{\rm\; ns}$. Then scattering produces a frequency modulation of the
observed intensity with a large bandwidth, $\Delta\nu\sim 1/\tau_{\rm
sc}\gtrsim 100{\rm\; MHz}$. Broadband frequency modulations observed in FRBs
could be due to scattering in a warm magnetar wind.
