The soliton connection |
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| Authors: | M. Crampin F. A. E. Pirani D. C. Robinson |
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| Affiliation: | (1) Faculty of Mathematics, The Open University, Walton Hall, Walton, Bletchley, Bucks, England;(2) Institute of Theoretical Physics, Warsaw University, ul. Ho!["zdot"]("/content/gm27781104497554/xlarge380.gif") a 69, Warsaw, Poland;(3) Present address: Department of Mathematics, King's College, Strand, WC2R 2LS London, England;(4) Dept. of Mathematics, King's College, Strand, WC2R 2LS London, England |
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| Abstract: | 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,  ). 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.On leave of absence. Visit supported by NSF Grant 36217 and by the Norman Foundation. |
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