Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 108, 10 pages      arXiv:2101.04332      https://doi.org/10.3842/SIGMA.2021.108

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

Received June 30, 2021, in final form December 13, 2021; Published online December 21, 2021

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.

Key words: quad-equation; NLS-type system; auto-Bäcklund transformation.

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