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arXiv · hep-th/9206002

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

Olivier Babelon·Denis Bernard
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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 $\hat {sl_2}$, and this gives the relation with the Bäcklund transformations, or using the level one representations of the affine Lie algebra $\widehat{sl_2}$, and this directly gives the formulae for the $τ$-functions in terms of vertex operators.

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Olivier Babelon, Denis Bernard. 1992-06-01. Affine Solitons: A Relation Between Tau Functions, Dressing and Bäcklund Transformations. https://doi.org/10.1142/s0217751x93000199

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