Periodic traveling waves of the regularized short pulse and Ostrovsky equations: Existence and stability

HAKKAEV S. A., Stanislavova M., Stefanov A.

SIAM Journal on Mathematical Analysis, cilt.49, sa.1, ss.674-698, 2017 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 1
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1137/15m1037901
  • Dergi Adı: SIAM Journal on Mathematical Analysis
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.674-698
  • Anahtar Kelimeler: Peakons, Regularized short pulse equation, Short pulse equation, Spectral stability, Traveling waves
  • Trakya Üniversitesi Adresli: Hayır

Özet

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.