Cylindrical freak waves in a non-Maxwellian dusty bulk-sheath plasma: An approximate solution for the cylindrical nonlinear Schrödinger equation

The properties of cylindrical dust ion-acoustic freak waves (FWs) are investigated in an unmagnetized collisionless dusty plasma in the presence of the sheath bulk model, which contain stationary negatively charged dust grains, nonthermal electrons, and inertial warm ions. For this purpose, the reductive perturbation method is used to reduce the fluid equations to a cylindrical Gardner/extended Korteweg–de Vries (CEKdV) equation. After that a cylindrical nonlinear Schrödinger equation (CNLSE) is obtained from the cylindrical EKdV using the derivative expansion method. The variation of the structural properties of the planar (one-dimensional) FWs with relevant plasma parameters is examined, in particular focusing on the temperature ratio of the ions-to-electrons, the fraction of negative charge residing on the dust and the nonthermal parameter. Moreover, the nonlinear dynamic of the sheath is obtain which may explain the solution of the exact analytical freak wave of the CNLSE using a suitable transformation.