Hakkaev, SevdzhanStanislavova, MilenaStefanov, Atanas G.2018-12-142018-12-142017Hakkaev, S., Stanislavova, M., & Stefanov, A. (2017). Periodic traveling waves of the regularized short pulse and Ostrovsky equations: existence and stability. SIAM Journal on Mathematical Analysis, 49(1), 674-698.https://hdl.handle.net/1808/27523We construct various periodic traveling wave solutions of the Ostrovsky/Hunter--Saxton/short pulse equation and its KdV regularized version. For the regularized short pulse model with small Coriolis parameter, we describe a family of periodic traveling 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 traveling peakons with corner crests. We show that the peakons are spectrally stable as well.© 2017, Society for Industrial and Applied MathematicsArticle10.1137/15M1037901openAccess