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

Orbital stability of periodic traveling-wave solutions for the regularized Schamel equation