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Multi-soliton solutions to the Thirring model through the reduction method

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It est démontré que la méthode de réduction appliquée à un système d'ordre 2×2 du type Zakharov-Shabat, muni d'une structure méromorphe appropriée, amène au modèle classique de Thirring; ce dernier étant de fait la condition d'intégrabilité du précédent système. Résuisant les transformations de Bäcklund génératrices de solitons, les solutions multi-solitons sont dérivées de manière explicite.

Abstract

It is shown how the reduction method applied to a 2×2 Zakharov-Shabat system with appropriate meromorphic structure leads to the Thirring model as integrability conditions. Reducing the generic soliton-generating multi-Bäcklund transformations, the general multi-soliton solutions are explicitly derived.

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Authors and Affiliations

  1. Centre de recherche de mathématiques appliquées, Université de Montreal, Case Postale 6128, Succ. ‘A’, H3C 3J7, Montreal, Canada

    D. David, J. Harnad & S. Shnider

Authors
  1. D. David
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  2. J. Harnad
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  3. S. Shnider
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Additional information

Research supported in part by the Natural Sciences and Engineering Research Council of Canada and an FCAC grant from the Ministère de l'Education du Gouvernement du Québec.

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David, D., Harnad, J. & Shnider, S. Multi-soliton solutions to the Thirring model through the reduction method. Lett Math Phys 8, 27–37 (1984). https://doi.org/10.1007/BF00420038

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  • DOI: https://doi.org/10.1007/BF00420038

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