Ukr. Mat. Zh. - 2012. - 64, № 10. - pp. 1365-1372
A new algebraic transformation method is constructed for finding traveling-wave solutions of complicated nonlinear wave equations on the basis of simpler ones. The generalized Dullin - Gottwald - Holm (DGH) equation and mKdV equations are chosen to illustrate our method. The solutions of the DGH equation can be obtained directly from solutions of the mKdV equation. Conditions under which different solutions appear are also given. Abundant traveling-wave solutions of the generalized DGH equation are obtained, including periodic solutions, smooth solutions with decay, solitary solutions, and kink solutions.