Kac-moody lie algebras and soliton equations. III. Stationary equations associated with A1 (1)

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Abstract

The Hamiltonian structure of stationary soliton equations associated with the AKNS eigenvalue problem is derived in two ways. First, it is shown to arise from the Kostant-Kirillov symplectic structure on a coadjoint orbit in an infinite-dimensional Lie algebra. Second, it is obtained as the restriction to a finite-dimensional manifold of the infinite-dimensional Hamiltonian structure associated with a certain eigenvalue problem polynomial in the eigenvalue parameter.

Original languageEnglish (US)
Pages (from-to)324-332
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Volume9
Issue number3
DOIs
StatePublished - 1983

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Hamiltonians
Soliton Equation
Kac-Moody Algebras
Hamiltonian Structure
Solitons
Algebra
Lie Algebra
algebra
eigenvalues
solitary waves
Polynomial Eigenvalue Problem
Infinite-dimensional Lie Algebras
Coadjoint Orbits
Symplectic Structure
Eigenvalue Problem
Orbits
Polynomials
Restriction
Eigenvalue
constrictions

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

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abstract = "The Hamiltonian structure of stationary soliton equations associated with the AKNS eigenvalue problem is derived in two ways. First, it is shown to arise from the Kostant-Kirillov symplectic structure on a coadjoint orbit in an infinite-dimensional Lie algebra. Second, it is obtained as the restriction to a finite-dimensional manifold of the infinite-dimensional Hamiltonian structure associated with a certain eigenvalue problem polynomial in the eigenvalue parameter.",
author = "Hermann Flaschka and Newell, {Alan C} and T. Ratiu",
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