Complete integrability of the Benjamin-Ono equation by means of action-angle variables

DOI10.1016/S0375-9601(97)00712-3zbMath0938.35159OpenAlexW2093722427MaRDI QIDQ1966549

Yanyan Li

Publication date: 8 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0375-9601(97)00712-3

zbMATH Keywords

action-angle variables of the BO equationGreen's function for the Lax operatorscattering problem for the Lax operator

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (10)

The Lyapunov stability of the N-soliton solutions in the Lax hierarchy of the Benjamin-Ono equation ⋮ Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study ⋮ Poisson structure and action-angle variables for the Hirota equation ⋮ High order conservative schemes for the generalized Benjamin-Ono equation on the unbounded domain ⋮ Numerical and perturbative computations of solitary waves of the Benjamin-Ono equation with higher order nonlinearity using Christov rational basis functions ⋮ On the Poisson structure and action-angle variables for the complex modified Korteweg-de Vries 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 ⋮ Bifurcations of new eigenvalues for the Benjamin–Ono equation

Cites Work

• Poisson structure for the KdV equation
• 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
• On the limit from the intermediate long wave equation to the Benjamin–Ono equation
• The scattering transform for the Benjamin-Ono equation
• Initial value problem of the linearized Benjamin–Ono equation and its applications
• The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems
• The Inverse Scattering Transform for the Benjamin–Ono Equation
• On the initial value problem for the modified Benjamin–Ono equation

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