The wave-particle interactions in a beam-plasma system in the presence of finite but small thermal motions of the particles are investigated in the linear as well as nonlinear regime. During the linear growth, the thermal motions are found to have a stabilizing effect. The nonlinear evolution is studied by using the Perturbed Orbit Formalism. Due to the thermal motions the nonlinear saturation of growth is found to take place at a level lower than that of the cold case. A detailed study of the energy balance shows that nonresonant particles pick up a bigger fraction of the energy lost by the streaming motion of the beam, thus leading to more efficient ‘heating’.

The nonlinear Schrödinger equation describing the evolution of the plane wave solutions of the Hirota equation and of the Boussinesq equation are obtained. The conditions for modulational instability and the localised stationary solutions are derived.

The envelope properties of ion-acoustic waves in a two-electron-temperature plasma are studied. The nonlinear Schrödinger equation describing the envelope of these waves is obtained from the plasma fluid equations by employing the Krylov-Bogoliubov-Mitropolsky perturbation method. It is shown that the ion-acoustic waves can be modulationally unstable or stable depending on the ratios of the densities and the temperatures of the hot and the cold electron components. Even a small fraction of the cold electron component can drastically affect the stability of the system.