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

DOI10.1137/15M1030649zbMath1338.35321arXiv1506.06110MaRDI QIDQ2798652

Yilun Wu

Publication date: 13 April 2016

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.06110

zbMATH Keywords

inverse scattering transformdiscrete spectrumspectral analysisBenjamin-Ono equationBirman-Schwinger boundFokas-Ablowitz transform

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Scattering theory of linear operators (47A40)

Related Items

Benjamin--Ono Soliton Dynamics in a Slowly Varying Potential Revisited, Crime pays; homogenization for long times, Complete integrability of the Benjamin-Ono equation on the multi-soliton manifolds, An explicit formula for the Benjamin-Ono equation, Zero-dispersion limit for the Benjamin-Ono equation on the torus with bell shaped initial data, Classification of traveling waves for a quadratic Szegö equation, Jost Solutions and the Direct Scattering Problem of the Benjamin--Ono Equation, Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE, Finite gap conditions and small dispersion asymptotics for the classical periodic Benjamin–Ono equation, A nonlinear Fourier transform for the Benjamin-Ono equation on the torus and applications, Long time behavior of solutions for a damped Benjamin-Ono equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the global well-posedness of the Benjamin-Ono equation
• Asymptotic behavior of solutions of the Korteweg-de Vries equation for large times
• Sur quelques généralisations de l'équation de Korteweg-de Vries
• Korteweg-de Vries equation; asymptotic behavior of solutions
• The bound state of weakly coupled Schrödinger operators in one and two dimensions
• On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations
• Perturbation theory for linear operators.
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Algebraic Solitary Waves in Stratified Fluids
• A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. I. Exact Two-Periodic Wave Solution
• On the zero-dispersion limit of the benjamin-ono cauchy problem for positive initial data
• The small dispersion limit of the korteweg-de vries equation. ii
• The small dispersion limit of the Korteweg-de Vries equation. III
• The small dispersion limit of the Korteweg-de Vries equation. I
• The scattering transform for the Benjamin-Ono equation
• The korteweg-de vries equation with small dispersion: Higher order lax-levermore theory
• The zero dispersion limit of the korteweg-de vries equation for initial potentials with non-trivial reflection coefficient
• On the cauchy problem for the benjamin-ono equation
• The zero dispersion limit for the Korteweg-deVries KdV equation
• GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H¹(R)
• The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems
• The Inverse Scattering Transform for the Benjamin–Ono Equation
• Fully nonlinear internal waves in a two-fluid system
• Internal waves of permanent form in fluids of great depth
• Solitary internal waves in deep water