Fundamental Properties of Dust Ion-Acoustic and Rogue Wave Analysis in Relativistic Dusty Plasmas

The collisionless, unmagnetized relativistic dusty plasma system comprising relativistic positively charged ions, energetic ion beams, and Maxwellian electrons is considered to study the fundamental properties of dust ion-acoustic waves (DIAWs) and formation of rogue waves (RWs). The Korteweg-de Vries (KdV) equation and nonlinear Schrödinger equation (NLSE) are derived using the well-known reductive perturbation and derivative expansion approaches, respectively. The concerned parameters play a crucial role in the fundamental properties (such as phase velocity, nonlinearity, dispersion, production, and propagation) of DIAWs. In addition, the rational solution of rogue waves (RWs) exists due to the effect of concerned parameters except the ion beam for argon.