Multi-dimensional integrable systems

  • R. S. Ward
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 280)


I began this lecture by posing the question of what the best way is to define integrability. The most promising definition seems to be one based on an associated overdetermined linear system which is “allowable”. The linear systems described in sections 3 and 4 are certainly allowable, and most known integrable equations can be obtained in this way. But there are exceptions, such as the KP equation, so the question is not yet settled. With this sort of definition, it would be difficult to establish whether or not a given equation was integrable. But one could try to classify all the integrable equations which arose from a certain type of linear system.


Consistency Condition Toda Lattice Cartan Matrix Overdetermined System Overdetermined Linear System 
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 1987

Authors and Affiliations

  • R. S. Ward
    • 1
  1. 1.Department of MathematicsDurham UniversityDurhamUK

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