New exact solutions to a new Hamiltonian amplitude equation

New exact solutions are obtained by means of the modified mapping method to a new Hamiltonian amplitude equation introduced by Wadati et al. [J. Phys. Soc. Jpn. 61 (1992) 1187]. The new periodic wave solutions are the linear combination of two different Jacobi elliptic waves. Limit cases are studied, and new solitary wave solution and triangular periodic wave solution are got.