Orbital stability of periodic travelingwave solutions for the regularized Schamel equation
Abstract
In this work we study the orbital stability of periodic travelingwave solutions for dispersive models. The study of traveling waves started in the mid18th 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 travelingwave 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.07181
 Bibcode:
 2015arXiv151207181P
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 to appear in Phys. D