Non-existence of internal mode for small solitary waves of the 1D Zakharov system
Abstract We prove that the linearised operator around any sufficiently small solitary wave of the one-dimensional Zakharov system has no internal mode. This spectral result, along with its proof, is expected to play a role in the study of the asymptotic stability of solitary waves.
Authors
- Yvan Martel (ORCID: https://orcid.org/0000-0002-3938-2451)
- Guillaume Rialland
Institutions
- Centre National de la Recherche Scientifique (FR)
- Institut Universitaire de France (FR)
- Université de Versailles Saint-Quentin-en-Yvelines (FR)
- Université Paris-Saclay (FR)
- Laboratoire de Mathématiques Blaise Pascal (FR)
Publication Details
- Journal
- Mathematische Annalen
- Published
- 2026-05-23
- DOI
- https://doi.org/10.1007/s00208-026-03492-8
- Primary Topic
- Advanced Mathematical Physics Problems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Université de Versailles Saint-Quentin-en-Yvelines