×

Some reductions of the self-dual Yang-Mills equations to integrable systems in \(2+1\) dimensions. (English) Zbl 0824.58054

Summary: A reduction of the self-dual Yang-Mills (SDYM) equations is studied by imposing two space-time symmetries and by requiring that the connection one-form belongs to a Lie algebra of formal matrix-valued differential operators in an auxiliary variable. In this article, the scalar case and the canonical cases for \(2\times 2\) matrices are examined. In the scalar case, it is shown that the field equations can be reduced to the forced Burgers equation. In the matrix case, several well-known 2+1 integrable equations are obtained. Also examined are certain transformation properties between the solutions of some of these 2+1 equations.

MSC:

58Z05 Applications of global analysis to the sciences
81T13 Yang-Mills and other gauge theories in quantum field theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1063/1.528014 · Zbl 0649.58042 · doi:10.1063/1.528014
[2] DOI: 10.1016/0375-9601(89)90964-X · doi:10.1016/0375-9601(89)90964-X
[3] DOI: 10.1007/BF01218161 · Zbl 0668.53048 · doi:10.1007/BF01218161
[4] DOI: 10.1063/1.529918 · Zbl 0744.58074 · doi:10.1063/1.529918
[5] DOI: 10.1063/1.529918 · Zbl 0744.58074 · doi:10.1063/1.529918
[6] DOI: 10.1007/BF02108076 · Zbl 0795.58027 · doi:10.1007/BF02108076
[7] DOI: 10.1016/0370-2693(78)90170-3 · doi:10.1016/0370-2693(78)90170-3
[8] DOI: 10.1007/BF01626514 · Zbl 0362.14004 · doi:10.1007/BF01626514
[9] DOI: 10.1088/0266-5611/3/1/009 · Zbl 0625.35073 · doi:10.1088/0266-5611/3/1/009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.