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Neumann Systems for the Algebraic AKNS Problem

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Neumann Systems for the Algebraic AKNS Problem Synopsis

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.

About This Edition

ISBN: 9780821825372
Publication date:
Author: Randolph J Schilling
Publisher: American Mathematical Society
Format: Paperback
Pagination: 59 pages
Series: Memoirs of the American Mathematical Society
Genres: Calculus and mathematical analysis