Investigation of Nonlinear Cylindrical Electrostatic Excitations in Dense Quantum Astrophysical Plasmas

It is imperative for many problems of physical interest to incorporate the geometrical curvature. Examples include plasma physics, oceanography, nonlinear optics, and laser-driven systems. Therefore, we consider planar wave propagation in a cylindrical geometry in light of the aforementioned applications, and the propagation is considered solely in the radial direction. Using the small amplitude perturbation approximation, the cylindrical Korteweg-de Vries (CKdV) equation is obtained using multiple-scale analysis to study nonlinear ion-acoustic waves in a dense plasma with electron trapping by incorporating the effects of the quantizing magnetic field and the smearing effects of the Fermi distribution function. The Bäcklund transformation is employed to obtain single and multiple soliton solutions of the CKdV equation, which are found to be very different from the planar KdV equation. A general mathematical framework is also presented to find the N-soliton solutions. The effects of the quantizing magnetic field and finite electron temperature on the structure of the cylindrical ion-acoustic solitons are also explored using the parameters representative of white dwarf stars. This research endeavor is expected to trigger interest in the plasma community to pursue this fascinating and abstruse research direction.