Effect of Dust Size Distribution Using the Nonlinear Schrödinger Equation in an Unmagnetized Dusty Plasma

This work derives the nonlinear Schrödinger equation (NLSE) for unmagnetized dusty plasmas using reductive perturbation methods, investigating the instability occurring in dust acoustic envelope waves. The analysis reveals the existence of stable dark envelope solitons and examines how dust particle size distributions influence wave dispersion characteristics. Our results demonstrate significant variations in solitary wave properties when comparing different size distribution models, including discontinuous and continuous power‐law distributions. Notably, for dust size ratios c > 1 (where c represents the maximum‐to‐minimum particle size ratio), plasmas with power‐law distributed particles exhibit greater solitary wave mass and velocity compared to those with uniform average‐sized particles. These findings provide important insights into nonlinear wave behavior in complex dusty plasma systems.