Abstract
In this paper, ansatz approach with the Jacobi elliptic functions is used to construct the solutions for the Zhiber–Shabat and related equation: Liouville equation, Dodd–Bullough–Mikhailov (DBM) equation, sinh–Gordon equation, and Tzitzeica–Dodd–Bullough (TDB) equation. Cnoidal, snoidal, triangular and periodic wave solutions for these equations are obtained. The constraint relations between the model coefficients and the damping coefficient for existence of soliton solutions are derived. The remarkable properties of the obtained solutions are showed in four interesting figures.
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