Investigation of exact solutions for the Tzitzéica type equations in nonlinear optics

Abstract

Abstract In this paper, we consider the Tzitzeica type equations and establish the travelling wave transformation which turns the nonlinear evolution equations into the ordinary differential equations, then we obtain exact solutions of the Tzitzeica-Dodd-Bullough equation, the Tzitzeica equation and the Dodd-Bullough-Mikhailov equation by using the exponential rational function method.