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Periodic Traveling Waves of the Regularized Short Pulse and Ostrovsky Equations: Existence and Stability
Hakkaev, Sevdzhan Stanislavova, Milena Stefanov, Atanas G.
Hakkaev, Sevdzhan
Stanislavova, Milena
Stefanov, Atanas G.
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Abstract
We 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.
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2017
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Society for Industrial and Applied Mathematics
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Hakkaev, 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.