Abstract
The cylindrical rogue wave (RW) and breathers in a collisionless, unmagnetized, and warm pair-ion plasma having thermal electrons and stationary negatively dust grains are investigated. The derivative expansion technique (DET) is employed for reducing the fluid equations of the mentioned plasma model to a cylindrical nonlinear Schrödinger equation (CNLSE). Posteriorly, for investigating the characteristics features of the cylindrical modulated structures including cylindrical RW and breathers, the CNLSE is solved analytically and numerically via high-accurate ansatz and numerical methods. Some approximate (analytical and numerical) solutions to the CNLSE are obtained for the first time. The ansatz methods is employed for deriving some semi-analytical solutions with high-accuracy. Also, the hybrid method of lines and the moving boundary method (MOL-MBM) is employed for analyzing the CNLSE numerically. A comparison between the approximate analytical and numerical simulation solutions is carried out. Furthermore, the residual maximum global error for the obtained approximate solutions is estimated. We are absolutely sure that this study will help all researchers to understand the mechanism of propagating cylindrical wave in various fields of science such as plasma physics, fluid mechanics, optical fiber, nonlinear optics. etc.