In a previous paper, we gave a correspondence between certain exact solutions to a \((2+1)\)-dimensional integrable Chiral Model and holomorphic bundles on a compact surface. In this paper, we use algebraic geometry to derive a closed-form expression for those solutions and show by way of examples how the algebraic data which parametrise the solution space dictates the behaviour of the solutions. Dans un article pr\'{e}c\'{e}dent, nous avons d\'{e}montr\'{e} que les solutions d'un mod\`{e}le chiral int\'{e}grable en dimension \( (2+1) \) correspondent aux fibr\'{e}s vectoriels holomorphes sur une surface compacte. Ici, nous employons la g\'{e}om\'{e}trie alg\'{e}brique dans une construction explicite des solutions. Nous donnons une formule matricielle et illustrons avec trois exemples la signification des invariants alg\'{e}briques pour le comportement physique des solutions.

Keywords:

integrable system, chiral field, sigma model, soliton, monad, uniton, harmonic map integrable system, chiral field, sigma model, soliton, monad, uniton, harmonic map

MSC Classifications:

35Q51 show english descriptions Soliton-like equations [See also 37K40] 35Q51 - Soliton-like equations [See also 37K40]

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