Exact and solitary wave solutions for the Tzitzeica–Dodd–Bullough and the modified KdV–Zakharov–Kuznetsov equations using the modified simple equation method

The modified simple equation (MSE) method is thriving in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in engineering and mathematical physics. In this study, we bring to bear the MSE method to look for the exact solutions via the Tzitzeica–Dodd–Bullough and the modified KdV–Zakharov–Kuznetsov equations involving parameters. When the parameters receive special values, solitary wave solutions are derived from the exact solutions. By means of this scheme, we found some fresh traveling wave solutions of the above mentioned equations.