Abstract
Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to sinh-Gördon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method are not true. Finally, we prove that our solutions to sinh-Gördon equation include all solutions obtained in the paper [Z.T. Fu, et al., Commun. Theor. Phys. (Beijing, China) 45 (2006) 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.