Bäcklund transformations and the construction of the Atiyah-Ward ansätze for self-dual SU(2) gauge fields |
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| Authors: | E Corrigan DB Fairlie RG Yates P Goddard |
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| Institution: | Department of Mathematics, University of Durham, UK;Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK |
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| Abstract: | Simple expressions for the ansätze of Atiyah and Ward are given in Yang's R gauge. Some non-linear transformations connecting solutions of the field equations are exhibited. These transformations are analogous to the Bäcklund transformations of the Sine-Gordon equation, etc., and provide an essentially algebraic inductive proof of the ansätze. Neither the sources for the anti-self-dual Maxwell fields used in the ansätze nor the reality conditions are discussed. |
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