A geometry for multidimensional integrable systems

✍ Scribed by I.A.B. Strachan

• Book ID: 104343388
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 975 KB
• Volume: 21
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(96)00019-8

✦ Synopsis

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 a 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 corresponds to taking the dispersionless limit in these hierarchies.