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Soliton Equations Extracted from the Noncommutative Zero-Curvature Equation

Takao Koikawa
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Abstract

We investigate the equation where the commutation relation in 2-dimensional zero-curvature equation composed of the algebra-valued potentials is replaced by the Moyal bracket and the algebra-valued potentials are replaced by the non-algebra-valued ones with two more new variables. We call the 4-dimensional equation the noncommutative zero-curvature equation. We show that various soliton equations are derived by the dimensional reduction of the equation.

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Takao Koikawa. 2001-01-11. Soliton Equations Extracted from the Noncommutative Zero-Curvature Equation. https://doi.org/10.1143/ptp.105.1045

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