The simplest equation approach for solving non-linear Tzitzeica type equations in non-linear optics

The aim of this work is to investigate new exact solutions of Tzitzeica type equations. We utilize the Painleve transformation to transform the aforesaid non-linear evolution equations into ordinary differential equations. Then, the simplest equation method is employed for securing some real and complex solutions of the Tzitzeica equation, the Tzitzeica-Dodd-Bullough equation and the Dodd-Bullough-Mikhailov equation. After the execution of the simplest equation method, we obtain many new results more simply and reliably than the other approaches executed on these equations. The solutions are obtained and verified through soft computations. Also, the dynamics of some solutions are presented via three types of graphs including 2D, 3D and contour graphs.