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

Mikhailov, Alexander V and Papamikos, Georgios and Wang, Jing Ping (2016) 'Darboux Transformation for the Vector Sine-Gordon Equation and Integrable Equations on a Sphere.' Letters in Mathematical Physics, 106 (7). 973 - 996. ISSN 0377-9017

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Abstract

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.

Item Type: Article
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 20 Jan 2020 14:23
Last Modified: 20 Jan 2020 14:23
URI: http://repository.essex.ac.uk/id/eprint/26520

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