Spectral stability of periodic waves for the Zakharov system
Journal of Mathematical Physics, vol.64, no.8, 2023 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 64 Issue: 8
- Publication Date: 2023
- Doi Number: 10.1063/5.0106133
- Journal Name: Journal of Mathematical Physics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, INSPEC, MathSciNet, zbMATH, DIALNET
- Trakya University Affiliated: Yes
Abstract
This paper is concerned with the stability of periodic traveling waves of dnoidal type, of the Zakharov system. This problem was considered in a study of Angulo and Brango [Nonlinearity 24, 2913 (2011)]. In particular, it was shown that under a technical condition on the perturbation, such waves are orbitally stable, with respect to perturbations of the same period. Our main result fills up the gap created by the aforementioned technical condition. More precisely, we show that for all natural values of the parameters, the periodic dnoidal waves are spectrally stable.