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Communications in Mathematical Physics

, Volume 274, Issue 3, pp 627–658 | Cite as

Coisotropic Deformations of Associative Algebras and Dispersionless Integrable Hierarchies

  • B. G. KonopelchenkoEmail author
  • F. Magri
Article

Abstract

The paper is an inquiry of the algebraic foundations of the theory of dispersionless integrable hierarchies, like the dispersionless KP and modified KP hierarchies and the universal Whitham hierarchy of genus zero. It stands out for the idea of interpreting these hierarchies as equations of coisotropic deformations for the structure constants of certain associative algebras. It discusses the link between the structure constants and Hirota’s tau function, and shows that the dispersionless Hirota bilinear equations are, within this approach, a way of writing the associativity conditions for the structure constants in terms of the tau function. It also suggests a simple interpretation of the algebro-geometric construction of the universal Whitham equations of genus zero due to Krichever.

Keywords

Structure Constant Associative Algebra Lagrangian Submanifolds Associativity Condition Integrable Hierarchy 
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 2007

Authors and Affiliations

  1. 1.Dipartimento di FisicaUniversita′ di Lecce and Sezione INFNLecceItaly
  2. 2.Dipartimento di Matematica ed ApplicazioniUniversita′ di Milano BicoccaMilanoItaly

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