### 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 language | English (US) |
---|---|

Pages (from-to) | 324-332 |

Number of pages | 9 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 9 |

Issue number | 3 |

DOIs | |

State | Published - 1983 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Statistical and Nonlinear Physics

### Cite this

**Kac-moody lie algebras and soliton equations. III. Stationary equations associated with A _{1}
^{(1)}
.** / Flaschka, Hermann; Newell, Alan C; Ratiu, T.

Research output: Contribution to journal › Article

_{1}

^{(1)}',

*Physica D: Nonlinear Phenomena*, vol. 9, no. 3, pp. 324-332. https://doi.org/10.1016/0167-2789(83)90275-0

}

TY - JOUR

T1 - Kac-moody lie algebras and soliton equations. III. Stationary equations associated with A1 (1)

AU - Flaschka, Hermann

AU - Newell, Alan C

AU - Ratiu, T.

PY - 1983

Y1 - 1983

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=4243532589&partnerID=8YFLogxK

U2 - 10.1016/0167-2789(83)90275-0

DO - 10.1016/0167-2789(83)90275-0

M3 - Article

AN - SCOPUS:4243532589

VL - 9

SP - 324

EP - 332

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3

ER -