Nonlinear lagrangian theory of envelope electrostatic plasma waves in a two-electron-temperature plasma

An analytical model based on Lagrangian variables was proposed to describe ion-acoustic wave propagating in an unmagnetized, collisionless, three-component plasma composed of inertial positive ions and two thermalized electron populations, characterized by different temperatures. It was shown that different types of localized envelope electrostatic excitations exist and their forms were analytically and numerically investigated in terms of the plasma dispersion and nonlinearly laws. The modulational stability of the amplitude of the propagating ion-acoustic oscillations was investigated. It was demonstrated that these electrostatic waves become unstable, due to self-interaction of the carrier wave.