Work

Non-existence of internal mode for small solitary waves of the 1D Zakharov system

Year: 2026

Type: article

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.

Source: Mathematische Annalen

DOI: 10.1007/s00208-026-03492-8

Authors: Yvan Martel, Guillaume Rialland

Institutions: Centre National de la Recherche Scientifique, Institut Universitaire de France, Université de Versailles Saint-Quentin-en-Yvelines, Université Paris-Saclay, Laboratoire de Mathématiques de Versailles

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Université de Versailles Saint-Quentin-en-Yvelines