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

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 N...

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Veröffentlicht in:	arXiv.org 2021-12
1. Verfasser:	Demskoi, Dmitry K
Format:	Artikel
Sprache:	eng
Schlagworte:	Formulas (mathematics) Liouville equations Physics - Exactly Solvable and Integrable Systems
Online-Zugang:	Volltext
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Zusammenfassung:	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.
ISSN:	2331-8422
DOI:	10.48550/arxiv.2101.04332