Open AccessSymmetry Reductions of the Lax Pair of the Four-Dimensional Euclidean Self-Dual Yang-Mills Equations
Author(s) -
Martin Legaré
Publication year - 1996
Publication title -
journal of nonlinear mathematical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.544
H-Index - 40
eISSN - 1776-0852
pISSN - 1402-9251
DOI - 10.2991/jnmp.1996.3.3-4.3
Subject(s) - mathematics , conjugacy class , lax pair , symmetry (geometry) , curvature , mathematical analysis , zero (linguistics) , symmetry group , euclidean geometry , differential equation , pure mathematics , partial differential equation , mathematical physics , geometry , integrable system , philosophy , linguistics
The reduction by symmetry of the linear system of the self-dual Yang-Millsequations in four-dimensions under representatives of the conjugacy classes ofsubgroups of the connected part to the identity of the corresponding Euclideangroup under itself is carried out. Only subgroups leading to systems ofdifferential equations nonequivalent to conditions of zero curvature withoutparameter, or to systems of uncoupled first order linear O.D.E.'s areconsidered. Lax pairs for a modified form of the Nahm's equations as well asfor systems of partial differential equations in two and three dimensions arewritten out.Comment: 27 pages, LaTeX209 fil
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