Bright-dark wave envelopes of nonlinear regularized-long-wave and Riemann wave models in plasma physics

Abstract

The nonlinear regularized-long-wave (RLW) and the Riemann wave (RW) models are physically significant in plasma physics and in further study of nonlinear dispersive waves, namely shallow water, ion-acoustic and magneto-sound waves in plasmas, anharmonic lattice and pressure waves in liquid-gas bubble mixtures, tidal and tsunami waves in rivers and oceans, longitudinal electromagnetic wave propagation in plasma, etc. The advanced generalized (G'/G)-expansion scheme is facilitated in this article for retrieving the bright-dark exact solitary wave solutions generated in the form of hyperbolic, trigonometric, and rational structures to the above-stated models. To figure out the internal contrivance of the solutions, 3D and contour plots concerning bright parabolic wave shape, compacton wave shape, bell-shaped soliton, kink wave type soliton, dark anti-parabolic wave shape, anti-compacton wave shape, bright propagation of solitary wave shape solutions are depicted for definite free parametric values. The characteristic feature of the wave envelops fluctuates taking into consideration the changes of free parameters and they are essentially dominated by the linear and nonlinear impact.