Symmetry Reductions of the Lax Pair of the Four-Dimensional Euclidean Self-Dual Yang-Mills Equations
arXiv:hep-th/9508093 · doi:10.2991/jnmp.1996.3.3-4.3
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.
27 pages, LaTeX209 file
References in corpus (1)
Cited by in corpus (13)
- Symmetries, Currents and Conservation Laws of Self-Dual Gravity
- Symmetries and Exact Solutions of Nonlinear Dirac Equations
- Bicomplexes and Integrable Models
- Spectral problem for a two-component nonlinear Schrödinger equation in dimensions: Singular manifold method and Lie point symmetries
- 1+1 spectral problems arising from the Manakov-Santini system
- Miura-reciprocal transformation and symmetries for the spectral problems of KdV and mKdV
- Classical Lie symmetries and reductions for a generalized NLS equation in 2+1 dimensions
- Symmetry and Exact Solutions of the Maxwell and SU(2) Yang-Mills Equations
- Classical Lie symmetries and reductions of a nonisospectral Lax pair
- Soliton equations in N-dimensions as exact reductions of the Self-Dual Yang-Mills equation V. Simplest (2+1)-dimensional soliton equations
- Spectral problem for the complex mKdV equation: singular manifold method and Lie symmetries
- Soliton equations in N-dimensions as exact reductions of Self-Dual Yang-Mills equation IV. The mM-LXII and Bogomolny equations
- Efficient Numerical Scheme for Solving (1+1), (2+1)-dimensional and Coupled Burgers Equation