*(English)*Zbl 0613.76129

This paper deals with coherent structures associated with Langmuir waves (longitudinal waves of electric field oscillating near the plasma frequency). In the 1-D adiabatic and Hamiltonian limit, the envelope of such waves obeys a simple cubic nonlinear Schrödinger (NLS) equation which possesses an exact (inverse scatter) solution. The marked changes in the properties of the nonlinear entities (solitons and breathers) were stressed in this paper.

In particular, the author discussed recent numerical and analytic results concerning: the effect on the 1-D cubic NLS equation, of introducing Landau damping at short scales and externally-driven instability at long scales; new results concerning self-similar solutions to the NLS equation in two dimensions; and a new mechanism for transfer of wave energy from long to short scales by wave-packet nucleation in density cavities, described by the Zaharov equations (the non-adiabatic generation of the NLS equations).

##### MSC:

76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |

35Q99 | PDE of mathematical physics and other areas |