Initial value problem of the linearized Benjamin–Ono equation and its applications

DOI10.1063/1.531953zbMath0891.35141OpenAlexW2087222174MaRDI QIDQ4379260

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Publication date: 25 February 1998

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531953

zbMATH Keywords

explicit solutionBenjamin-Ono equationlarge time asymptoticscompleteness relation for the eigenfunctionsstability of the \(N\)-soliton solution

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Solitary waves for incompressible inviscid fluids (76B25)

Related Items (15)

The Lyapunov stability of the N-soliton solutions in the Lax hierarchy of the Benjamin-Ono equation ⋮ On the existence of solitary waves for an internal system of the Benjamin-Ono type ⋮ Exact Controllability and Stabilization for Linear Dispersive PDE’s on the Two-Dimensional Torus ⋮ Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE ⋮ Complete integrability of the Benjamin-Ono equation by means of action-angle variables ⋮ On the Benjamin-Ono equation in the half line ⋮ Complete eigenfunctions of linearized integrable equations expanded around a soliton solution ⋮ Linear stability of multiple dark solitary wave solutions of a nonlocal nonlinear Schrödinger equation for envelope waves ⋮ On the controllability and stabilization of the linearized Benjamin-Ono equation ⋮ Bifurcations of new eigenvalues for the Benjamin–Ono equation ⋮ Transverse instability and collapse of internal algebraic solitary waves in fluids of large depth ⋮ Benjamin-Ono equation with unbounded data ⋮ Control and stabilization of the Benjamin-Ono equation on a periodic domain ⋮ Structure of linearization operators of the Korteweg-de Vries hierarchy equations expanded around single-soliton solutions ⋮ The renormalization method for singular perturbation of solitons

Cites Work

• The Benjamin-Ono-Burgers equation: An application in solar physics
• Expansions with respect to squares, symplectic and Poisson structures associated with the Sturm-Liouville problem. I
• Closure of the squared Zakharov-Shabat eigenstates
• Linear stability of multiple internal solitary waves in fluids of great depth
• Algebraic Solitary Waves in Stratified Fluids
• Bäcklund Transform and Conservation Laws of the Benjamin-Ono Equation
• Completeness of Derivatives of Squared Schrödinger Eigenfunctions and Explicit Solutions of the Linearized K<scp>d</scp>V Equation
• A New Form of Backlund Transformations and Its Relation to the Inverse Scattering Problem
• Linear stability of internal wave solitons in a deep stratified fluid
• Slowly varying solitary waves in deep fluids
• Evolution Equations for Long, Nonlinear Internal Waves in Stratified Shear Flows
• Exact multi-soliton solution of the Benjamin-Ono equation
• Internal waves of permanent form in fluids of great depth
• Solitary internal waves in deep water
• Long nonlinear waves in stratified shear flows

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