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The complex Sine-Gordon equation as a symmetry flow of the AKNS Hierarchy
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.Comment: 8 pages, LaTeX, typos corrected, references update
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