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 variablecoefficient 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.

A numerical study of third-order equation with time-dependent coefficients: KdVB equation

“…On the other hand, by introducing variable coefficients α(t) > 0 and β(t) > 0, the KdVB equation (2.1) is useful to describe solitonic propagation in fluids [38], a variety of cosmic plasma phenomena [15,26,36,16], among others. Motivated by those applications and as mentioned, as far as we know, an exhaustive numerical study for (2.1) has not been reported.…”

Local exact controllability to the trajectories of the Korteweg–de Vries–Burgers equation on a bounded domain with mixed boundary conditions

“…The system (1) can be viewed as a model of propagation of long water waves in channels of shallow depth, whose solutions depend on the nonlinearity, dispersion, and dissipation. Moreover, by introducing a variable coefficient ν(t), the KdVB equation ( 1) is useful to describe cosmic plasmas phenomena [18], [27]. Respect to the boundary conditions, they appear in order to symmetry the operator.…”

Analytical multi-soliton solutions of a (2+1)-dimensional breaking soliton equation

“…In recent years, many research have studied soliton and its evolvements in nonlinear equations via kinds of method (Zarmi 2014 ; Chen and Ma 2013 ; Ashorman 2014 ; Zhang and Chen 2016 ; Meng and Gao 2014 ; Mohamed 2016 ; Liu and Liu 2016 ; Jiang and Ma 2012 ; Guo and Hao 2013 ; Dou et al 2007 ). Vertex dynamics in multi-soliton solutions and some new exact solution of breaking equation are studied in Zarmi ( 2014 ) and Chen and Ma ( 2013 ), the methods of Multi-soliton Solutions are given in Ashorman ( 2014 ), Zhang and Chen ( 2016 ), Meng and Gao ( 2014 ), Mohamed ( 2016 ), Liu and Liu ( 2016 ), Jiang and Ma ( 2012 ), Guo and Hao ( 2013 ), Dou et al ( 2007 ), Zuo and Gao ( 2014 ), Huang ( 2013 ), Liu and Luo ( 2013 ), Côtea and Muñoza ( 2014 ), Xu and Chen ( 2014 ), Hua and Chen ( 2014 ) and Zhang and Cai ( 2014 ), complex solutions for the [BLP System are proposed in Ma and Xu ( 2014 )], and these so-called new solutions is identical to the universal formula in Doungmo Goufo ( 2016 ), Atangana and Doungmo Goufo ( 2015 ), Gao ( 2015a , b , c , d ), Xie and Tian ( 2015 ), Sun and Tian ( 2015 ) and Zhen et al ( 2015 ).…”