Dust-acoustic Gardner solitons in cryogenic plasma with the effect of polarization in the presence of a quantizing magnetic field

A theoretical investigation is presented for dust-acoustic (DA), Gardner solitons (GSs), and double layers (DLs) in a magnetized cryogenic plasma system. The plasma consists of inertial negatively charged dust, Boltzmann distributed electrons, and ions, all existing in a quantizing magnetic field. The Korteweg–de Vries (KdV), a modified KdV (mKdV), and Gardner equations are derived by using the reductive perturbation method. It is found that the KdV solitons and DLs are either compressive or rarefactive depending on the plasma parameters, whereas only compressive mKdV and rarefactive GSs solitons exist. These GSs and DLs are significantly modified due to the introduction of the polarization force effect. The present results are considered to be beneficial in understanding the waves propagating at cryogenic temperatures in the experiments of the nano-electromechanical application such as cryogenic etching of silicon that leads to etched silicon and makes it highly anisotropic with a high etch rate, lower side etching, and increases the dry etch resistance of organic masks.