  Fast radio bursts (FRBs) are mysterious radio transients whose physical
origin is still unknown. Within a few astronomical units near an FRB source,
the electric field of the electromagnetic wave is so large that the electron
oscillation velocity becomes relativistic, which makes the classical Thomson
scattering theory and the linear plasma theory invalid. We discuss FRBs as
strong waves interacting with the ambient medium, in terms of both electron
motion properties and plasma properties. Several novel features are identified.
1. The cross section of Thomson scattering is significantly enhanced for the
scattering photons. 2. On the other hand, because of the nonlinear plasma
properties in strong waves, the near-source plasma is more transparent and has
a smaller effective dispersion measure (DM) contribution to the observed value.
For a repeating FRB source, the brighter bursts would have somewhat smaller DMs
contributed by the near-source plasma. 3. The radiation beam undergoes
relativistic self-focusing in a dense plasma, the degree of self-focusing (or
squeezing) depends on the plasma density. Such a squeezing effect would affect
the collimation angle and the true event rate of FRBs. 4. When an FRB
propagates in a nearby ambient plasma, a wakefield wave in the plasma will be
generated by the ponderomotive force of the FRB and accelerates electrons in
the ambient medium. However, such an effect is too weak to be observationally
interesting.
