The tan h method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations

The tan h method is applied to the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations. Solitons and periodic solutions for these equations are formally derived. The Painlevé property v = e±u will be employed to back up our analysis and to emphasize the effectiveness of the presented method.