Site menu:

Information:

This paper has been submitted for publication in the Annals of Mathematics. To download a preprint of this paper just click here.

This material is based upon work supported by the National Science Foundation under Grant Nos. DMS-2204896 and DMS-2508694. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF).

Search box:



A proof of the soliton resolution conjecture for the Benjamin-Ono equation

Louise Gassot, Patrick Gérard, and Peter D. Miller

LG: CNRS and Department of Mathematics, University of Rennes, Rennes, France
PG: Laboratoire de Mathématiques d'Orsay, Université Paris-Saclay, Orsay, France
PDM: Department of Mathematics, University of Michigan, Ann Arbor

Abstract:

We give a proof of the soliton resolution conjecture for the Benjamin-Ono equation, namely every solution with sufficiently regular and decaying initial data can be written as a finite sum of soliton solutions with different velocities up to a radiative remainder term in the long-time asymptotics. We provide a detailed correspondence between the spectral theory of the Lax operator associated to the initial data and the different terms of the soliton resolution expansion. The proof is based on a new use of a representation formula of the solution due to the second author, and on a detailed analysis of the distorted Fourier transform associated to the Lax operator.