Scattering theory for the Korteweg-de Vries (KdV) equation and its Hamiltonian interpretation

DOI10.1016/0167-2789(86)90186-7zbMath0618.35100OpenAlexW1977099635MaRDI QIDQ1822275

L. A. Takhtadzhyan, Vladimir S. Buslaev, Ludvig Faddeev

Publication date: 1986

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(86)90186-7

zbMATH Keywords

continuous spectrumnonlinear Schrödinger equationKorteweg-de Vries equationscattering transformToda chainHamiltonian formulation

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Partial differential equations of mathematical physics and other areas of application (35Q99) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (13)

Integrability of nonlinear dynamical systems and differential geometry structures ⋮ Boundary values as Hamiltonian variables. I. New Poisson brackets ⋮ Monodromy dependence and connection formulae for isomonodromic tau functions ⋮ Formulation of scattering theory for the nonlinear Schrödinger equation with boundary conditions of the finite density type in a soliton-free sector ⋮ On the mathematical work of Vladimir Savel′evich Buslaev ⋮ Who cares about integrability? ⋮ \(N\)-soliton strings in four-dimensional space-time ⋮ Toda lattice with a special self-consistent source ⋮ Poisson structure and action-angle variables for the Camassa-Holm equation ⋮ Boundary terms and their Hamiltonian dynamics ⋮ Approximating pseudopotentials for evolution equations containing a small parameter ⋮ Geometry of KdV. IV: Abel sums, Jacobi variety, and theta function in the scattering case ⋮ Boundary conditions and confinement in the gauge field theory at finite temperature

Cites Work

• Inverse problem of quantum scattering theory. II
• Asymptotic Solutions of the Korteweg-deVries Equation
• A simple model of the integrable Hamiltonian equation
• Method for Solving the Korteweg-deVries Equation
• Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian System
• The spectral theory of a functional-difference operator in conformal field theory
• Unnamed Item
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