The sine-Gordon expansion method to look for the traveling wave solutions of the Tzitzéica type equations in nonlinear optics

In this paper, using the Painleve property, the traveling wave transformation, and the sine-Gordon expansion method (SGEM), the Tzitzéica type evolution equations in nonlinear optics, including the Tzitzéica equation, the Dodd-Bullough-Mikhailov (DBM) equation, the Tzitzéica-Dodd-Bullough (TDB) equation, and the Liouville equation are studied. As a result, a series of traveling wave solutions for the Tzitzéica type equations are obtained. The efficiency of the solution methodology in exactly solving nonlinear evolution equations is confirmed.