The paper presents two of the methods that can be used in finding traveling wave solutions for various models with nonlinear dynamics: the _functional expansion_ and the _attached flow_ methods. Both of them contain quite original approaches and an interesting potential in getting analytical solutions for a large class of difficult to solve nonlinear partial differential equations.
The two methods are compared with similar approaches appearing in literature, their strengths and limitations being pointed out. Three important models of nonlinear partial differential equations with applications in physics are considered as examples, their traveling wave solutions being interpreted in terms of the soliton theory. The considered models are the Gardner, the Fisher and the Tzitzeica equations.