ON IMMERSION FORMULAS FOR SOLITON SURFACES

Authors

  • Alfred Michel Grundland Université du Québec à Trois-Rivières & Centre de recherches mathématiques
  • Decio Levi Dipartimento di Mathematica e Fisica dell’Università Roma Tre, Sezione INFN di Roma Tre, Via della Vasca Navale 84, Roma, 00146 Italy
  • Luigi Martina

DOI:

https://doi.org/10.14311/AP.2016.56.0180

Keywords:

Integrable systems, Soliton surfaces, Immersion formulas, Generalized symmetries

Abstract

This paper is devoted to a study of the connections between three different analytic descriptions for the immersion functions of 2D-surfaces corresponding to the following three types of symmetries: gauge symmetries of the linear spectral problem, conformal transformations in the spectral parameter and generalized symmetries of the associated integrable system. After a brief exposition of the theory of soliton surfaces and of the main tool used to study classical and generalized Lie symmetries, we derive the necessary and sufficient conditions under which the immersion formulas associated with these symmetries are linked by gauge transformations. We illustrate the theoretical results by examples involving the sigma model.

Downloads

Download data is not yet available.

Author Biography

  • Luigi Martina
    Dipartimento di Mathematica e Fisica dell’Università del Salento, Sezione INFN di Lecce, Via Arnesano, C.P.
    193 Lecce, 73100 Italy

Downloads

Published

2016-06-30

Issue

Vol. 56 No. 3 (2016)

Section

Articles

License

Authors who publish with this journal agree to the following terms:

1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).

4. ddd

How to Cite

Grundland, A. M., Levi, D., & Martina, L. (2016). ON IMMERSION FORMULAS FOR SOLITON SURFACES. Acta Polytechnica, 56(3), 180-192. https://doi.org/10.14311/AP.2016.56.0180