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The soliton connection

✍ Scribed by M. Crampin; F. A. E. Pirani; D. C. Robinson

Book ID
104768841
Publisher
Springer
Year
1977
Tongue
English
Weight
211 KB
Volume
2
Category
Article
ISSN
0377-9017

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✦ Synopsis

It is pointed out that the linear scattering problem for a non-linear evolution equation which admits soliton solutions may be described in terms of a linear connection on a principal SL(2, N)-bundle. The equation in question is satisfied if and only if the curvature of this connection vanishes. Some other properties of the curvature are identified. The sine-Gordon, Korteweg-de Vries and modified Korteweg-de Vries equations are treated explicitly.

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