The (G′G)-expansion method for Tzitzéica type nonlinear evolution equations

In this work, the (G′G)-expansion method is applied for constructing more general exact solutions of the three nonlinear evolution equations with physical interest namely, the Tzitzéica equation, the Dodd–Bullough–Mikhailov (DBM) equation and the Tzitzéica–Dodd–Bullough (TDB) equation. Our work is motivated by the fact that the (G′G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.