INTRODUCTION.

In an unmagnetized plasma, three kinds of waves can propagate. These are the ion-acoustic, electron plasma, and light waves. The linear dispersion relations of these waves are, respectively, given by

where cs is the sound speed, ƛDis the electron Debye length, is the s 1) electron plasma frequency, and c is the velocity of light.

The most important role of nonlinear effects is to cause steepening of the leading edge of a wave. However, it is frequently found that the dispersion effects become significant as the steepness of the front increases. The competition between nonlinearity and dispersion leads to localized waves often called “solitons”.

In the present article, we review theories of solitons in an unmagnetized plasma. To understand the physics, we have chosen three simple waves (as given above) and have worked out nonlinear theories for them. As is well-known (Sagdeev, 1966), supersonic compresslonal ion-acoustic solitons have a maximum potential ∼ 1.3 Te/e, and the corresponding speed is about 1.6 cs. On the other hand, finite amplitude envelope Langmuir and light wave solitons are obtained by incorporating a fully nonlinear analysis of the low-frequency plasma motion. It is found that under certain circumstances, equations governing the stationary solitons are exactly integrable and can be written in terms of the energy integral of a classical particle. By analogy with the motion of an oscillator in a potential well, we analyze the conditions under which localized solutions exist. Our theory of Langmuir wave envelope solitons compares favorably with laboratory experiments. In the small amplitude limit, a perturbation theory has been introduced which enables us to derive a set of nonlinear evolution equations describing Langmuir soliton turbulence. A new kind of electromagnetic soliton emerges when the relativistic corrections to the nonlinear current density and the ponderomotive force are taken into account. Here, the forced electron density perturbation contains a depression at the center, together with shoulders of density excess on the sides. Such kinds of nonlinear entities can effectively accelerate electrons in plasma.