Exact closed form solutions of compound Kdv Burgers’ equation by using generalized (G?/G) expansion method

Abstract

In this investigation, the compound Korteweg-de Vries (Kd-V) Burgers equation with constant coefficients is considered as the model, which is used to describe the properties of ion-acoustic waves in plasma physics, and also applied for long wave propagation in nonlinear media with dispersion and dissipation. The aim of this paper to achieve the closed and dynamic closed form solutions of the compound KdV Burgers equation. We derived the completely new solutions to the considered model using the generalized (G?/G)-expansion method. The newly obtained solutions are in form of hyperbolic and trigonometric functions, and rational function solutions with inverse terms of the trigonometric, hyperbolic functions. The dynamical representations of the obtained solutions are shown as the annihilation of three-dimensional shock waves, periodic waves, and multisoliton through their three dimensional and contour plots. The obtained solutions are also compared with previously exiting solutions with both analytically and numerically, and found that our results are preferable acceptable compared to the previous results.