Spectral stability of periodic waves for the Zakharov system-Reference-Cited by-同舟云学术

Spectral stability of periodic waves for the Zakharov system

Published:2023-08-01 Issue:8 Volume:64 Page:
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:

Author:

Hakkaev Sevdzhan¹²^ORCID,Stanislavova Milena³^ORCID,Stefanov Atanas G.³^ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science, Trakya University 1 , 22030 Edirne, Türkiye

2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences 2 , Acad. G. Bonchev Str. bl. 8, 1113 Sofia, Bulgaria

3. Department of Mathematics, University of Alabama - Birmingham 3 , 1402 10th Avenue South, Birmingham, Alabama 35294, USA

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.

Funder

National Science Foundation

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0106133/18079242/081503_1_5.0106133.pdf

Reference18 articles.

1. Collapse of Langmuir waves;Sov. Phys. JETP,1972

2. The stability of solitary waves;Proc. R. Soc. London, Ser. A,1972

3. On the stability theory of solitary waves;Proc. R. Soc. London, Ser. A,1975

4. Sufficient conditions for stability of solitary-wave solutions of model equations for long waves;Physica D,1987

5. Total positivity and the stability of internal waves in stratified fluids of finite depth;IMA J. Appl. Math.,1991