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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 108, 10 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.108 (Mi sigma1790) 		 
The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System

Dmitry K. Demskoi

School of Computing, Mathematics and Engineering, Charles Sturt University,NSW 2678, Australia
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DOI: https://doi.org/10.3842/SIGMA.2021.108
Abstract: We treat the lattice sine-Gordon equation and two of its generalised symmetries as a compatible system. Elimination of shifts from the two symmetries of the lattice sine-Gordon equation yields an integrable NLS-type system. An auto-Bäcklund transformation and a superposition formula for the NLS-type system is obtained by elimination of shifts from the lattice sine-Gordon equation and its down-shifted version. We use the obtained formulae to calculate a superposition of two and three elementary solutions.
Keywords: quad-equation, NLS-type system, auto-Bäcklund transformation.
Received: June 30, 2021; in final form December 13, 2021; Published online December 21, 2021
Bibliographic databases:
Document Type: Article
MSC: 35Q51, 35Q55, 37K60
Language: English
Citation: Dmitry K. Demskoi, “The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System”, SIGMA, 17 (2021), 108, 10 pp.
Citation in format AMSBIB
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