Neumann systems for the algebraic AKNS problem / Randolph J. Schilling.

Format:

Book

Author/Creator:

Schilling, Randolph J. (Randolph James), 1951- author.

Series:

Memoirs of the American Mathematical Society ; Volume 97, Number 467.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 97, Number 467

Language:

English

Subjects (All):

Hamiltonian systems.

Evolution equations.

Jacobians.

Physical Description:

1 online resource (79 p.)

Edition:

1st ed.

Other Title:

AKNS problem.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1992.

Language Note:

English

Summary:

The Neumann system, an algebraically completely integrable Hamiltonian system, consists of harmonic oscillators constrained to move on the unit spere in configuration space. Any finite gap potential of Hill's equation may be expressed in terms of a solution of the Neumann problem. The present work is concerned with an algebraically completely integrable Hamiltonian system whose solutions may be used to describe the finite gap solutions of the AKNS spectral problem, a first order two-by-two matrix linear system. Trace formulas, constraints, Lax paris, and constants of motion are obtained using Krichever's algebraic inverse spectral transform. Computations are carried out explicityly over the class of spectral problems with square matrix coefficients.

Contents:

""Table of Contents""; ""Introduction""; ""Chapter I. The Geometry of Neumann Systems""; ""Chapter II. A Neumann System for the AKNS Problem""; ""Chapter III. The Divisor Map""; ""Chapter IV. Hamiltonian Formalism""; ""Appendix: The Neumann System""; ""Bibliography""

Notes:

"May 1992, Volume 97, Number 467 (first of 3 numbers)."

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-0893-7