Exact peaked wave solution of CH-γ equation by the first-integral method

By using the first-integral method, which is based on the ring theory of commutative algebra, an exact peaked wave solution to CH-γ equation has been obtained directly. The obtained solution agrees well with the previously known one in the literature. However, the first-integral method is easier and quicker than other traditional techniques. This indicates that the validity and great potential of the first-integral method in solving complicated solitary wave problems.