  In this work we study the orbital stability of periodic traveling-wave
solutions for dispersive models. The study of traveling waves started in the
mid-18th century when John S. Russel established that the flow of water waves
in a shallow channel has constant evolution. In recent years, the general
strategy to obtain orbital stability consists in proving that the traveling
wave in question minimizes a conserved functional restricted to a certain
manifold. Although our method can be applied to other models, we deal with the
regularized Schamel equation, which contains a fractional nonlinear term. We
obtain a smooth curve of periodic traveling-wave solutions depending on the
Jacobian elliptic functions and prove that such solutions are orbitally stable
in the energy space. In our context, instead of minimizing the augmented
Hamiltonian in the natural codimension two manifold, we minimize it in a "new"
manifold, which is suitable to our purposes.
