A geometry for multidimensional integrable systems

Strachan, I.A.B. (1997) A geometry for multidimensional integrable systems. Journal of Geometry and Physics, 21(3), pp. 255-278. (doi: 10.1016/S0393-0440(96)00019-8)

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A deformed differential calculus is developed based on an associative ★-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one obtains a geometric description of the operators. A dual theory is also possible, based on deformation of differential forms. This calculus is applied to a number of multidimensional integrable systems such as the KP hierarchy, thus obtaining a geometrical description of these systems. The limit in which the deformation disappears correspond to taking the dispersionless limit in these hierarchies.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Strachan, Professor Ian
Authors: Strachan, I.A.B.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Geometry and Physics
ISSN (Online):1879-1662
Published Online:19 May 1998

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