Noncommutative Korteweg-de-Vries Equation
Aristophanes Dimakis, Folkert Muller-Hoissen
TL;DR
This paper introduces a noncommutative version of the KdV equation, constructed through deformation quantization, which retains integrability features and relates to the classical KdV via a Seiberg-Witten map.
Contribution
It presents the first formulation of a noncommutative KdV equation with conserved densities and links to classical solutions through a Seiberg-Witten map.
Findings
Constructed a deformation quantized ncKdV with infinite conserved densities
Derived solutions of ncKdV from classical KdV solutions
Established a noncommutative Miura transformation connecting ncKdV variants
Abstract
We construct a deformation quantized version (ncKdV) of the KdV equation which possesses an infinite set of conserved densities. Solutions of the ncKdV are obtained from solutions of the KdV equation via a kind of Seiberg-Witten map. The ncKdV is related to a modified ncKdV equation by a noncommutative Miura transformation.
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Advanced Topics in Algebra · Black Holes and Theoretical Physics