Stability of periodic travelling shallow-water waves determined by Newton's equation
Stability of periodic travelling shallow-water waves determined by Newton's equation
We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin–Bona–Mahony and Camassa–Holm equations. To prove orbital stability, we use the abstract results of Grillakis–Shatah–Strauss and the Floquet theory for periodic eigenvalue problems.