  We propose a simple algebraic method for generating classes of traveling wave
solutions for a variety of partial differential equations of current interest
in nonlinear science. This procedure applies equally well to equations which
may or may not be integrable. We illustrate the method with two distinct
classes of models, one with solutions including compactons in a class of models
inspired by the Rosenau-Hyman, Rosenau-Pikovsky and Rosenau-Hyman-Staley
equations, and the other with solutions including peakons in a system which
generalizes the Camassa-Holm, Degasperis-Procesi and Dullin-Gotwald-Holm
equations. In both cases, we obtain new classes of solutions not studied
before.
