Explicit solutions of the nonlinear partial differential equations

The convection and diffusion process or their mixed states are the important phenomena in the different physical systems. In order to understand these physical processes, the nonlinear differential equations, Fisher, Burger–Fisher, Benjamin–Bona–Mahony–Burgers (BBMB) and Modified Benjamin–Bona–Mahony (MBBM) are solved to obtain the traveling wave solutions using (G′G)-expansion method. In this study we give the exact solutions of these equations which describe the dynamics of turbulence created by the interaction of matters. Our solutions are reduced to the well-known solutions in the literature assigning some special values to the constants in the solutions of these equations. Moreover, we have reached the new exact solutions for these equations mentioned above. We have also analyzed and plotted the results using different integration constants to understand the behavior of solutions.