Symmetry Reductions of the Lax Pair of the Four-Dimensional Euclidean Self-Dual Yang-Mills Equations

DOI

10.2991/jnmp.1996.3.3-4.3How to use a DOI?

Abstract

The reduction by symmetry of the linear system of the self-dual Yang-Mills equations in four-dimensions under representatives of the conjugacy classes of subgroups of the connected part to the identity of the corresponding Euclidean group under itself is carried out. Only subgroups leading to systems of differential equations nonequivalent to conditions of zero curvature without parameter, or to systems of uncoupled first order linear O.D.E.'s are considered. Lax pairs for a modified form of the Nahm's equations as well as for systems of partial differential equations in two and three dimensions are written out.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - M. Legaré
PY  - 1996
DA  - 1996/09/02
TI  - Symmetry Reductions of the Lax Pair of the Four-Dimensional Euclidean Self-Dual Yang-Mills Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 266
EP  - 285
VL  - 3
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1996.3.3-4.3
DO  - 10.2991/jnmp.1996.3.3-4.3
ID  - Legaré1996
ER  -