Noncommutative Korteweg-de-Vries Equation

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.

10 pages, 3 figures

References in corpus (3)

• A Geometry for Multidimensional Integrable Systems
• Bi-differential calculi and integrable models
• A Noncommutative Version of the Nonlinear Schrodinger Equation

Cited by in corpus (13)

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• On non commutative sinh-Gordon Equation
• Soliton Scattering in Noncommutative Spaces
• Quasideterminant solutions of NC Painlevé II equation with the Toda solution at $n=1$ as a seed solution in its Darboux transformation
• Explicit Flow Equations and Recursion Operator of the ncKP hierarchy
• Conserved Quantities in Noncommutative Principal Chiral Model with Wess-Zumino Term
• Lax pair representation and Darboux transformation of NC Painlevé-II equation
• Darboux solutions of non-abelian quantum Painlevé II equation in terms of quasideterminants