English

The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System

Exactly Solvable and Integrable Systems 2021-12-22 v3

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-B\"acklund 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

Cite

@article{arxiv.2101.04332,
  title  = {The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System},
  author = {Dmitry K. Demskoi},
  journal= {arXiv preprint arXiv:2101.04332},
  year   = {2021}
}