Abstract
•We present application in mathematical physics models.•Higher order first and second order PDE equations.•Solitary wave solutions.•The hydrodynamic mathematical methods•Modulation instability analysis.
The propagation of waves in dispersive media, liquid flow containing gas bubbles, fluid flow in elastic tubes, oceans and gravity waves in a smaller domain, spatio-temporal rescaling of the nonlinear wave motion are delineated by the compound Korteweg-de Vries (KdV)-Burgers equation, the (2+1)-dimensional Maccari system and the generalized shallow water wave equation. In this work, we effectively derive abundant closed form wave solutions of these equations by using the double (G′/G, 1/G)-expansion method. The obtained solutions include singular kink shaped soliton solutions, periodic solution, singular periodic solution, single soliton and other solutions as well. We show that the double (G′/G, 1/G)-expansion method is an efficient and powerful method to examine nonlinear evolution equations (NLEEs) in mathematical physics and scientific application.