Dissipative Kawahara ion-acoustic solitary and cnoidal waves in a degenerate magnetorotating plasma

The two-dimensional fluid quantum hydrodynamic (QHD) is adopted as the basis for a discussion of the effects of Landau quantization magnetic field, the Coriolis force, and collisional frequency on the (non)linear properties of the dissipative ion-acoustic waves (IAWs). By employing the reductive perturbation technique (RPT), the damped Korteweg-de Vries (KdV) equation which contains the lowest perturbation order actions is derived. It was found that with an increase in amplitude, the soliton width and the velocity diverge from the prediction of the damped KdV equation as observed in some laboratory experiments, i.e. the damped KdV approximation becomes invalid to describe the system. Therefore, it is necessary to investigate the effect of higher-order which leads to the damped Kawahara equation. This equation is a completely non-integrable differential equation. Thus, a new approximate solution which is called a semi-analytical solution is derived in detail. The obtained results can help in understanding the features of quantum IAWs in dense and slowly rotating astrophysical plasmas and maybe understand the quantum Hall effect of novel materials like graphene and topological insulators.