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Resonant Geometric Phases for Soliton Equations

Alber, M. S. and Marsden, J. E. (1994) Resonant Geometric Phases for Soliton Equations. In: Hamiltonian and Gradient Flows, Algorithms and Control. Fields Institute Communications. No.3. American Mathematical Society , Providence, RI, pp. 1-26. ISBN 978-0-8218-0255-7.

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The goal of the present paper is to introduce a multidimensional generalization of asymptotic reduction given in a paper by Alber and Marsden [1992], to use this to obtain a new class of solutions that we call resonant solitons, and to study the corresponding geometric phases. The term "resonant solitons" is used because those solutions correspond to a spectrum with multiple points, and they also represent a dividing solution between two different types of solitons. In this sense, these new solutions are degenerate and, as such, will be considered as singular points in the moduli space of solitons.

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Additional Information:©1994, American Mathematical Society. Mark Alber thanks The Fields Institute for its kind hospitality during two visits in 1993. We also thank Dave McLaughlin for several helpful suggestions.
Funding AgencyGrant Number
Ministry of Colleges and Universities of OntarioUNSPECIFIED
Natural Sciences and Engineering Research Council of CanadaUNSPECIFIED
Series Name:Fields Institute Communications
Issue or Number:3
Classification Code:1991 MSC: Primary 58F07; Secondary 70H99
Record Number:CaltechAUTHORS:20101011-104457907
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20367
Deposited By: Ruth Sustaita
Deposited On:23 Nov 2010 18:21
Last Modified:03 Oct 2019 02:09

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