By using reductive perturbation technique we have studied the linear and non-linear properties of ion-acoustic solitary structures in a three-component plasma containing non-thermal electrons and Boltzmann positrons and a comparatively cold ion which has got a streaming motion. The Korteweg–de Vries equation has been obtained and the dependence of small amplitude solitary structures on various plasma parameters such as streaming velocity (v₀), non-thermal parameter (β), reciprocal of electron temperature (χ), positron density (p), Mach number (M), and ion density (δ) have been studied. The possibility of formation of enveloping soliton and its characteristic features are further investigated by deriving the non-linear Schrödinger equation.

In the work, we study the formation of electron acoustic Korteweg-de Vries (KdV) solitons and their gradual nonlinear evolution into a peregrine soliton (PS) in a dense plasma at finite temperature with quantum effects. The plasma under consideration has temperature anisotropy along the direction of wave propagation. Such an anisotropy is due to the initial disturbance incorporated in the system or due to the lack of homogeneity of field quantities. We have studied both the linear and nonlinear characteristics of their dispersion relation. By employing reductive perturbation technique, we have obtained the KdV equation and studied the characteristics of the solitary structures. The effect of external forcing term which leads to self-interaction among different parts of the system and the gradual conversion of the waveform into Peregrine breather mode is analytically studied. Finally, we study the dynamical properties of the system and its dependence on plasma parameters. This theoretical study will help in predicting possible characteristics in laser plasma interaction and beam plasma experiments in which there are instances of temperature anisotropy.