A variety of nonlinear effects occur in a plasma. First, there are
the wave steepening effects which can occur in any fluid in which
the propagation speed depends upon the wave-amplitude. In a
dispersive medium this can lead to classes of nonlinear waves which
may have stationary solutions like solitons and shocks. Because the
plasma also acts like an inherently nonlinear dielectric resonant
interactions among waves lead to exchange of energy among them.
Further, an electromagnetic wave interacting with a plasma may
parametrically excite other waves in the plasma. A large-amplitude
Langmuir wave undergoes a modulational instability which arises
through local depressions in plasma density and the corresponding
increases in the energy density of the wave electric field. Whereas
a field collapse occurs in two and three dimensions, in a
one-dimensional case, spatially localized stationary field
structures called Langmuir solitons can result. Many other plasma
waves like upper-hybrid waves, lower-hybrid waves etc. can also
undergo a modulational instability and produce localized field
structures. A new type of nonlinear effect comes into play when an
electromagnetic wave propagating through a plasma is strong enough
to drive the electrons to relativistic speeds. This leads to a
propagation of an electromagnetic wave in a normally overdense
plasma, and the coupling of the electromagnetic wave to a Langmuir
wave in the plasma. The relativistic mass variation of the
electrons moving in an intense electromagnetic wave can also lead
to a modulational instability of the latter."
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