Verification of Extended Dark Envelope Solitons in Dusty Plasma

In this work, we investigate the formation and propagation of extended dark envelope solitary waves in an unmagnetized, collisionless dusty plasma composed of negatively charged dust grains, electrons, and two‐temperature ions. Starting from the fluid and Poisson equations, the nonlinear Schrödinger equation (NLSE) governing dust‐acoustic waves is derived via the multiple‐scale perturbation method, and a generalized non‐exact dark soliton solution with adjustable parameters is introduced to examine amplitude and localization effects. Particle‐in‐Cell (PIC) simulations are conducted to verify the analytical results, showing excellent agreement and confirming the stability and persistence of the dark soliton under parameter variations, thereby providing a solid theoretical and numerical foundation for nonlinear wave dynamics in dusty plasmas.