Affine Solitons: A Relation Between Tau Functions, Dressing and Bäcklund Transformations

1992/06/01 by Olivier Babelon, Denis Bernard · 1 citation
Physics and Astronomy · #hep-th

paper · pdf · doi:10.1142/s0217751x93000199

published as Int.J.Mod.Phys.A8:507-543,1993 · 33 pages. SPhT-92-055; LPTHE-92-16

arxiv created 1992/06/01 · arxiv updated 2009/11/30

Abstract

We reconsider the construction of solitons by dressing transformations in the sine-Gordon model. We show that the N-soliton solutions are in the orbit of the vacuum, and we identify the elements in the dressing group which allow us to built the N-soliton solutions from the vacuum solution. The dressed τ-functions can be computed in two different ways~: either using adjoint actions in the affine Lie algebra sl₂, and this gives the relation with the Bäcklund transformations, or using the level one representations of the affine Lie algebra \widehatsl₂, and this directly gives the formulae for the τ-functions in terms of vertex operators.

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