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II. Mathematical Structures

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Synergetics

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 2))

Abstract

The history of this subject is that GARDNER, GREENE, KRUSKAL and MIURA [34] suggested the inverse scattering scheme of solution for the KdV (22) in 1967, ZAKHAROV and SHABAT (ZS) [35] solved the NLS (24) in 1971, and WADATI and TODA [36] used the method of [34] to find the explicit solution of the KdV whilst WADATI [37] used the method of ZS [35] to solve the modified KdV (23) in 1972. Then HIROTA [38] and CAUDREY, GIBBON, EILBECK and BULLOUGH [39] found the multisoliton solutions of the s-G in 1972–73 and these were rapidly followed by the inverse scattering solution by ABLOWITZ, KAUP, NEWELL and SEGUR (AKNS) [40]. AKNS then gave a generalised ZS inverse scattering scheme [16]. Most of the work of this paper II is concerned with the AKNS-ZS scheme.

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Authors
  1. R. K. Bullough
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  2. R. K. Dodd
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Editors and Affiliations

  1. Institut für Theoretische Physik, der Universität Stuttgart, Pfaffenwaldring 57/IV, D-7000, Stuttgart 80, Fed. Rep. of Germany

    Hermann Haken

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Bullough, R.K., Dodd, R.K. (1977). II. Mathematical Structures. In: Haken, H. (eds) Synergetics. Springer Series in Synergetics, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66784-8_11

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  • DOI: https://doi.org/10.1007/978-3-642-66784-8_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-66786-2

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