The noncommutative sine-Gordon breather
Andre Fischer, Olaf Lechtenfeld
TL;DR
This paper constructs and analyzes noncommutative deformations of the sine-Gordon model, focusing on breather solutions and their properties, including explicit corrections due to noncommutativity.
Contribution
It introduces a method to explicitly construct noncommutative sine-Gordon breathers using the dressing method adapted for Moyal deformation, providing concrete results and visualizations.
Findings
Noncommutative breather solutions maintain temporal periodicity.
Explicit first-order noncommutative corrections to breathers are derived.
Plots illustrate the impact of noncommutativity on breather configurations.
Abstract
As shown in [hep-th/0406065], there exists a noncommutative deformation of the sine-Gordon model which remains (classically) integrable but features a second scalar field. We employ the dressing method (adapted to the Moyal-deformed situation) for constructing the deformed kink-antikink and breather configurations. Explicit results and plots are presented for the leading noncommutativity correction to the breather. Its temporal periodicity is unchanged.
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