On the linear stability of simple and semi-simple periodic waves for a system of cubic Klein–Gordon equations

HAKKAEV S. A., Syuleymanov T.

Mathematische Nachrichten, cilt.296, sa.5, ss.1886-1900, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 296 Sayı: 5
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1002/mana.202100352
  • Dergi Adı: Mathematische Nachrichten
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.1886-1900
  • Anahtar Kelimeler: linear stability, nonlinear wave equation, periodic traveling waves
  • Trakya Üniversitesi Adresli: Hayır

Özet

We study the linear stability of traveling wave solutions for the nonlinear wave equation and coupled nonlinear wave equations. It is shown that periodic waves of the dnoidal type are spectrally unstable with respect to co-periodic perturbations. Our arguments rely on a careful spectral analysis of various self-adjoint operators, both scalar and matrix and on instability index count theory for Hamiltonian systems.