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The complex Sine-Gordon equation as a symmetry flow of the AKNS Hierarchy

H. Aratyn·L. A. Ferreira·J. F. Gomes·A. H. Zimerman
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Abstract

It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the ``negative'' symmetry flows forming the Borel loop algebra. The complex sine-Gordon and the vector Nonlinear Schrodinger equations appear as lowest negative and second positive flows within the extended hierarchy. This is fully analogous to the well-known connection between the sine-Gordon and mKdV equations within the extended mKdV hierarchy. A general formalism for a Toda-like symmetry occupying the ``negative'' sector of sl(N) constrained KP hierarchy and giving rise to the negative Borel sl(N) loop algebra is indicated.

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H. Aratyn, L. A. Ferreira, J. F. Gomes, A. H. Zimerman. 2000-08-31. The complex Sine-Gordon equation as a symmetry flow of the AKNS Hierarchy. https://doi.org/10.1088/0305-4470%2F33%2F35%2F101

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