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

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-Bäcklund transformation and a superposition formula for the NLS-type...

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Veröffentlicht in:Symmetry, integrability and geometry, methods and applications integrability and geometry, methods and applications, 2021-01
1. Verfasser: Demskoi, Dmitry K.
Format: Artikel
Sprache:eng
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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-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.
ISSN:1815-0659
1815-0659
DOI:10.3842/SIGMA.2021.108