Semi-analytical solution of dissipative rogue waves and breathers in nonthermal plasma

Abstract This work examines the propagation of dissipative dust-ion-acoustic (DIA) waves in a plasma with non-thermal electrons, heated positive ions, and stationary negative dust particles. This discussion also includes dissipative rogue waves (DRWs) and breathers. The linear damped nonlinear Schrödinger equation (dNLSE) and its detailed derivation are described here. When it comes to differential equations, the dNLSE is believed to be one that cannot be integrated. As a result of this, even with the inclusion of the linear damping term, there is still no solution that is accurate. In light of this, we will proceed to meticulously derive and present the semi-analytical solution today. This method allows for the analytical solution of the fundamental nonlinear Schrödinger equation (NLSE), with the damping term being left out of the equation. Using this method as a starting point, one can begin the process of solving the linearly damped NLSE. In addition to this, we will evaluate the analytical solutions of the standard NLSE in comparison to the approximate analytical solutions of the dNLSE. The manner in which plasma properties influence the characteristics of dissipatively modulated DIA waves is the subject of extensive research. To be more specific, the nonthermal electron count, the kinematic viscosity of the ions, and the temperature ratio of the ions to electrons are all taken into consideration. There is a possibility that this work will shed light on the modulated DIA structures that are present in both laboratory plasmas and space plasmas, as well as make predictions regarding such structures.