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Geometry of the akns — ZS inverse scattering scheme

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Nonlinear Evolution Equations and Dynamical Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 120))

Abstract

We review the geometrical theory of nonlinear evolution equations (NEEs) solvable by the AKNS1-generalised Zakharov-Shabat2 scattering problem introduced by one of us previously3,4. We show how the theory contains within it the canonical structure known to be associated with integrable NEEs. We exploit the “gaugerd transformations of the geometric theory to derive an infinite set of non-local Hamiltonian densities for the sine-Gordon equation. We show that it is from these that the hierarchy of Lax-type sine-Gordon equations can be derived. We summarise the relation between the geometric theory and the theory of prolungation structures due to Wahlquist and Estabrook.

On leave from Department of Mathematics, U.M.I.S.T., P.O. Box 88, Manchester M60 10,D, England.

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Author information

Authors and Affiliations

  1. Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen 0, Denmark

    R. Sasaki

  2. Nordita, Blegdamsvej 17, DK-2100, Copenhagen, Denmark

    R. K. Bullough

Authors
  1. R. Sasaki
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  2. R. K. Bullough
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Editor information

M. Boiti F. Pempinelli G. Soliani

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© 1980 Springer-Verlag

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Sasaki, R., Bullough, R.K. (1980). Geometry of the akns — ZS inverse scattering scheme. In: Boiti, M., Pempinelli, F., Soliani, G. (eds) Nonlinear Evolution Equations and Dynamical Systems. Lecture Notes in Physics, vol 120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09971-9_44

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  • DOI: https://doi.org/10.1007/3-540-09971-9_44

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  • Print ISBN: 978-3-540-09971-0

  • Online ISBN: 978-3-540-39197-5

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