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.

Section 3.4 has been rewritten to correct a flaw