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). pp. 973-996. DOI https://doi.org/10.1007/s11005-016-0855-5
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). pp. 973-996. DOI https://doi.org/10.1007/s11005-016-0855-5
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). pp. 973-996. DOI https://doi.org/10.1007/s11005-016-0855-5
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 |
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Uncontrolled Keywords: | the vector sine-Gordon equation; Lax representations; Darboux transformations; Backlund transformations; Yang-Baxter maps; integrable equations on a sphere |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 20 Jan 2020 14:23 |
Last Modified: | 07 Aug 2024 18:26 |
URI: | http://repository.essex.ac.uk/id/eprint/26520 |
Available files
Filename: vSG_darbouxmws.pdf