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arXiv · 2101.04332

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

Dmitry K. Demskoi
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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.

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Dmitry K. Demskoi. 2021-01-12. The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System. https://doi.org/10.3842/sigma.2021.108

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