Variety of the cosmic plasmas: General variable-coefficient Korteweg-de Vries-Burgers equation with experimental/observational support

Abstract

Plasmas are known as the most abundant form of matter in the Universe. Nowadays, with respect to the cosmic plasmas, considerable efforts have been put into investigating the experimentally relevant Korteweg-de Vries (KdV)-Burgers–type equations. In this letter, with plenty of experimental/observational support presented, symbolic computation on a general variable-coefficient KdV-Burgers equation is performed, which covers the models for a variety of the cosmic plasmas. An auto-Bäcklund transformation is constructed out, along with two families of the analytic solitonic solutions, for the electrostatic wave potential, perturbation of the magnitude of the magnetic field, fluctuation of electron or ion density, or radial-direction component of the velocity of ions or dust particles. Both our auto-Bäcklund transformation and solitonic solutions depend on the cosmic-plasma parameters by way of the nonlinearity, dispersion, dissipation and geometric-effect coefficient functions, as to the ion-acoustic, magnetoacoustic, electron-acoustic, positron-acoustic, dust-acoustic and quantum dust-ion-acoustic waves. The shock structures from our analytic investigation agree well with to those experimentally reported. Certain effects of a cosmic-plasma system, described by such variable coefficients, might be detected by the future plasma experiments/observations.