Simplicity and Finiteness of Discrete Spectrum of the Benjamin-Ono Scattering Operator

2015/06/19 by Yilun Wu, Wu, Yilun · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Spectral Theory in Mathematical Physics #math.AP

paper · pdf · doi:10.48550/arxiv.1506.06110

19 pages

openalex publication_date 2015/06/19 · arxiv created 2015/11/01 · arxiv updated 2015/11/03 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

A spectral analysis is done on the L operator of the Lax pair for the Benjamin-Ono equation. Simplicity and finiteness of the discrete spectrum are established as are needed for the Fokas and Ablowitz inverse scattering transform scheme. A crucial step in the simplicity proof is the discovery of a new identity connecting the L² norm of the eigenvector to its inner product with the scattering potential. The proof for finiteness is an extension of the ideas involved in the Birman-Schwinger bound for Schrödinger operators.

Cited by

• Orbital stability of Benjamin--Ono multisolitons

Related

• Direct Scattering for the Benjamin-Ono Equation with Rational Initial Data
• Jost Solutions and the Direct Scattering Problem of the Benjamin--Ono Equation
• Lax eigenvalues in the zero-dispersion limit for the Benjamin-Ono equation on the torus
• Operator splitting for the Benjamin-Ono equation
• On the spectrum of the Lax operator of the Benjamin-Ono equation on the torus