## Abstract

Treating the lattice sine-Gordon equation, along with its two simplest generalized symmetries, as a compatible system allows one to investigate another integrable system not directly connected to the sine-Gordon equation: a modified non-linear Schrödinger system with derivative.

The first step involves eliminating shifts from the two symmetries of the lattice sine-Gordon equation, resulting in the NLS-type system. Subsequently, an auto-Bäcklund transformation and a superposition formula for the NLS-type system are obtained by eliminating shifts from both the lattice sine-Gordon equation and its down-shifted version. We employ the derived formulas to calculate a superposition of two and three elementary solutions.

The first step involves eliminating shifts from the two symmetries of the lattice sine-Gordon equation, resulting in the NLS-type system. Subsequently, an auto-Bäcklund transformation and a superposition formula for the NLS-type system are obtained by eliminating shifts from both the lattice sine-Gordon equation and its down-shifted version. We employ the derived formulas to calculate a superposition of two and three elementary solutions.

Original language | English |
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Publication status | Published - 01 Dec 2023 |

Event | Eleventh Workshop on Integrable Systems 2023 - University of Sydney, Sydney, Australia Duration: 30 Nov 2023 → 01 Dec 2023 https://www.maths.usyd.edu.au/u/integrable/programme.html https://austms.org.au/event/11th-workshop-on-integrable-systems/ (Event information) |

### Workshop

Workshop | Eleventh Workshop on Integrable Systems 2023 |
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Country/Territory | Australia |

City | Sydney |

Period | 30/11/23 → 01/12/23 |

Other | The eleventh workshop on Integrable Systems will be held at the School of Mathematics and Statistics at the University of Sydney on 30 November – 1 December 2023. This year we expect again a very exciting meeting with many interesting presentations. The workshop is organised by Harini Desiraju, Nalini Joshi, Milena Radnovic, Pieter Roffelsen. |

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