Jost Solutions and the Direct Scattering Problem of the Benjamin--Ono Equation

DOI10.1137/17M1124528zbMath1398.35140arXiv1704.01692MaRDI QIDQ4602198

Yilun Wu

Publication date: 9 January 2018

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

Full work available at URL: https://arxiv.org/abs/1704.01692

zbMATH Keywords

inverse scattering transformBenjamin-Ono equationJost solutionsscattering datacompletely integrable

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Scattering theory for PDEs (35P25) Transform methods (e.g., integral transforms) applied to PDEs (35A22)

Related Items (12)

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study ⋮ 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 ⋮ Asymptotic \(N\)-soliton-like solutions of the fractional Korteweg-de Vries equation ⋮ Zero-dispersion limit for the Benjamin-Ono equation on the torus with bell shaped initial data ⋮ Unconditional uniqueness for 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 ⋮ Benjamin–Ono soliton dynamics in a slowly varying potential ⋮ 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
• On the global well-posedness of the Benjamin-Ono equation
• Sur quelques généralisations de l'équation de Korteweg-de Vries
• On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations
• Complete integrability of the Benjamin-Ono equation by means of action-angle variables
• The scattering transform for the Benjamin-Ono equation in the small-dispersion limit
• Simplicity and Finiteness of Discrete Spectrum of the Benjamin--Ono Scattering Operator
• Algebraic Solitary Waves in Stratified Fluids
• A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. I. Exact Two-Periodic Wave Solution
• Direct Scattering for the Benjamin-Ono Equation with Rational Initial Data
• The scattering transform for the Benjamin-Ono equation
• On the cauchy problem for the benjamin-ono 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

This page was built for publication: Jost Solutions and the Direct Scattering Problem of the Benjamin--Ono Equation