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-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
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Formulas (mathematics)
Liouville equations
Physics - Exactly Solvable and Integrable Systems
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description 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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Physics - Exactly Solvable and Integrable Systems
title The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System
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