Transverse instability for periodic waves of KP-I and schrödinger equations

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

Indiana University Mathematics Journal, cilt.61, sa.2, ss.461-492, 2012 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 61 Sayı: 2
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1512/iumj.2012.61.4558
  • Dergi Adı: Indiana University Mathematics Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.461-492
  • Anahtar Kelimeler: KP-I equation, Periodic traveling waves, Schrödinger equation, Transverse instability
  • Trakya Üniversitesi Adresli: Hayır

Özet

We consider the quadratic and cubic KP-I and NLS models in 1 + 2 dimensions with periodic boundary conditions. We show that the spatially periodic traveling waves (with period K) in the form u(t,x,y) = φ(x-ct) are spectrally and linearly unstable when the perturbations are taken to be with the same period. This strong instability implies other instabilities considered recently-for example, with respect to perturbations with periods nK, n = 2, 3,... or bounded perturbations.