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

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

2000-07-02

arxiv.org/abs/nlin/0007002v3

J.Phys. A33 (2000) L331-339

Nonlinear Sciences

Exactly Solvable and Integrable Systems

8 pages, LaTeX, typos corrected, references updated

Scientific paper

10.1088/0305-4470/33/35/101

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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