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Toward a Topological Classification of Integrable PDE’s

  • Nicholas M. Ercolani
  • David W. McLaughlin
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 22)

Abstract

We model Fomenko’s topological classification of 2 degree of freedom integrable stratifications in an infinite dimensional soliton system. Specifically, the analyticity of the Floquet discriminant Δ(q, ») in both of its arguments provides a transparent realization of a Bott function and of the remaining building blocks of the stratification; in this manner, Fomenko’s structure theorems are expressed through the inverse spectral transform. Thus, soliton equations are shown to provide natural representatives of the classification in the context of PDE’s.

Keywords

Double Point Integrable Hamiltonian System Soliton Equation Topological Classification Critical Circle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1991

Authors and Affiliations

  • Nicholas M. Ercolani
    • 1
  • David W. McLaughlin
    • 2
  1. 1.Department of MathematicsUnivesity of ArizonaTucsonUSA
  2. 2.Department of Mathematics Program in Applied and Computational MathematicsPrinceton UniversityPrincetonUSA

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