New exact traveling wave solutions of the Tzitzéica-type evolution equations arising in non-linear optics

The properties of Tzitzéica equations in non-linear optics have been the subject of many recent studies. In this article, a new and effective modification of Kudryashov method is adopted to study this class of non-linear evolution equations. As an achievement, new exact traveling wave solutions of Tzitzéica, Dodd–Bullough–Mikhailov (DBM) and Tzitzéica–Dodd–Bullough (TDB) equations are formally extracted. It is believed that the modified Kudryashov method along with the symbolic computation package suggests a promising technique to handle non-linear evolution equations in non-linear optics.