Darboux Transformation for the Vector Sine-Gordon Equation and Integrable Equations on a Sphere

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• 作者：Alexander V. Mikhailov ; Georgios Papamikos…
• 刊名：Letters in Mathematical Physics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：106
• 期：7
• 页码：973-996
• 全文大小：585 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Statistical Physics
  Geometry
  Group Theory and Generalizations
  
• 出版者：Springer Netherlands
• ISSN：1573-0530
• 卷排序：106

文摘

We propose a method for construction of Darboux transformations, which is a new development of the dressing method for Lax operators invariant under a reduction group. We apply the method to the vector sine-Gordon equation and derive its Bäcklund transformations. We show that there is a new Lax operator canonically associated with our Darboux transformation resulting an evolutionary differential-difference system on a sphere. The latter is a generalised symmetry for the chain of Bäcklund transformations. Using the re-factorisation approach and the Bianchi permutability of the Darboux transformations, we derive new vector Yang–Baxter map and integrable discrete vector sine-Gordon equation on a sphere.Keywordsthe vector sine-Gordon equationLax representationsDarboux transformationsBäcklund transformationsYang–Baxter mapsintegrable equations on a sphere