Periodic Traveling Waves of the Regularized Short Pulse and Ostrovsky Equations: Existence and Stability

We construct various periodic travelling wave solutions of the Ostrovsky/HunterSaxton/short pulse equation and its KdV regularized version. For the regularized short pulse model with small Coriolis parameter, we describe a family of periodic travelling waves which are a perturbation of appropriate KdV solitary waves. We show that these waves are spectrally stable. For the short pulse model, we construct a family of travelling peakons with corner crests. We show that the peakons are spectrally stable as well.