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Article Dans Une Revue International Journal of Modern Physics A Année : 2012

AFFINE SOLITONS: A RELATION BETWEEN TAU FUNCTIONS, DRESSING AND BÄCKLUND TRANSFORMATIONS

Olivier Babelon
  • Fonction : Auteur
Denis Bernard

Résumé

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 build 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 [Formula: see text], and this gives the relation with the Bäcklund transformations, or using the level-one representations of the affine Lie algebra [Formula: see text], and this directly gives the formulae for the τ functions in terms of vertex operators.

Dates et versions

hal-03370745 , version 1 (08-10-2021)

Identifiants

Citer

Olivier Babelon, Denis Bernard. AFFINE SOLITONS: A RELATION BETWEEN TAU FUNCTIONS, DRESSING AND BÄCKLUND TRANSFORMATIONS. International Journal of Modern Physics A, 2012, 08 (03), pp.507-543. ⟨10.1142/S0217751X93000199⟩. ⟨hal-03370745⟩
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