Abstract
In this paper, we present the sine-Gordon expansion method to prepare the mixed dark bright wave patterns to the nonlinear partial differential equations arising in mathematical physics. Then, we apply the proposed method for a credible recourse of two nonlinear physical models: the modified Vakhnenko-Parkes and modified a-equation. These exact solutions comprise the hyper-bolic, trigonometric, rational and exponential function with few licentious parameter. The analyt-ical solutions have different physical structures and they are graphically analyzed in order to show their dynamical behavior by means of 2D, 3D and contour plots. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).