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The soliton connection

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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, ℝ). 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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Author notes

  1. F. A. E. Pirani

    Present address: Department of Mathematics, King's College, Strand, WC2R 2LS, London, England

Authors and Affiliations

  1. Faculty of Mathematics, The Open University, Walton Hall, Walton, Bletchley, Bucks, England

    M. Crampin

  2. Institute of Theoretical Physics, Warsaw University, ul. Hoża 69, Warsaw, Poland

    F. A. E. Pirani

  3. Dept. of Mathematics, King's College, Strand, WC2R 2LS, London, England

    D. C. Robinson

Authors
  1. M. Crampin
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  2. F. A. E. Pirani
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  3. D. C. Robinson
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Additional information

On leave of absence. Visit supported by NSF Grant 36217 and by the Norman Foundation.

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Crampin, M., Pirani, F.A.E. & Robinson, D.C. The soliton connection. Lett Math Phys 2, 15–19 (1977). https://doi.org/10.1007/BF00420665

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  • DOI: https://doi.org/10.1007/BF00420665

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