Publicação: The complex sine-Gordon equation as a symmetry flow of the AKNS hierarchy
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2000-09-08
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Iop Publishing Ltd
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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 the sl(N) constrained KP hierarchy and giving rise to the negative Borel sl(N) loop algebra is indicated.
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Journal of Physics A-mathematical and General. Bristol: Iop Publishing Ltd, v. 33, n. 35, p. L331-L337, 2000.
