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Towards a Multi-Hamiltonian Theory of (2+1)-Dimensional Field Systems

  • Maciej Blaszak
Chapter
Part of the Texts and Monographs in Physics book series (TMP)

Abstract

The last chapter of this book is devoted to the algebraic theory of (2 + 1)-dimensional field systems. The reason why the algebraic theory of integrable field systems in multidimensions is remarkably different from that in one space dimension was an important observation made in 1985 by Konopelchenko and Zakharov [195]. Actually, they proved that for (n + 1)-dimensional field theory for n > 1 there are no recursion operators expressible by pseudo-differential matrix operators as for the (1 + 1) case. As a consequence, there are no second Poisson structures in the same form. Hence, one can try to find them only in the form of bilocal objects, i.e. in a kernel representation, for example. It makes the algebraic theory of integrable field (lattice) systems in multidimensions more complex when compared to these in one space dimension.

Keywords

Poisson Structure Auxiliary Field Noncommutative Variable AKNS Hierarchy Commute Vector Field 
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 Berlin Heidelberg 1998

Authors and Affiliations

  • Maciej Blaszak
    • 1
  1. 1.Physics DepartmentA. Mickiewicz UniversityPoznańPoland

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