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Lax Triples for Integrable Surfaces in Three-Dimensional Space

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  • Jan L. Cieśliński
  • Artur Kobus

Abstract

We study Lax triples (i.e., Lax representations consisting of three linear equations) associated with families of surfaces immersed in three-dimensional Euclidean space . We begin with a natural integrable deformation of the principal chiral model. Then, we show that all deformations linear in the spectral parameter are trivial unless we admit Lax representations in a larger space. We present an explicit example of triply orthogonal systems with Lax representation in the group . Finally, the obtained results are interpreted in the context of the soliton surfaces approach.

Suggested Citation

  • Jan L. Cieśliński & Artur Kobus, 2016. "Lax Triples for Integrable Surfaces in Three-Dimensional Space," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-8, July.
    • Handle: RePEc:hin:jnlamp:8386420
    DOI: 10.1155/2016/8386420
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