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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Abstract
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 |
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Status: | Published |
Refereed: | Yes |
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 |
Publisher: | Elsevier |
ISSN: | 0393-0440 |
ISSN (Online): | 1879-1662 |
Published Online: | 19 May 1998 |
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