28 citations · 51 across the 7 of their papers we have counts for
7 papers
On a set of Grassmann-valued extensions of systems of ordinary differential equations
M. Legare
Formulations of some Grassmann-valued systems of ordinary differential equations invariant under (infinitesimal) supersymmetry transformations, including -superspace extended ty…
Comments on non-commuting variables, n-ary algebras, and first-order differential equations
M. Legare
Use of certain non-commuting variables is considered in first-order differential equations. Superspace variables are discussed within the setting of first-order ordinary differenti…
On Certain Quantization Aspects of (Generalized) Toda Systems
M. Legare
Ordinary and gl(n,R) generalized Toda systems as well as a related hierarchy are probed with respect to certain quantization characteristics. "Quantum" canonical and Poisson transf…
Non-Abelian monopole equations with zero curvature and self-dual Yang-Mills theories
M. Legare
A version of non-Abelian monopole equations is explored through dimensional reductions, with often the addition of algebraic conditions. On zero curvature spaces, spinor related ex…
Noncommutative Generalized NS and Super Matrix KdV Systems from a Noncommutative Version of (Anti-) Self-Dual Yang-Mills Equations
M. Legare
A noncommutative version of the (anti-) self-dual Yang-Mills equations is shown to be related via dimensional reductions to noncommutative formulations of the generalized (SO(3)/SO…
Super-Matrix KdV and Super-Generalized NS Equations from Self-Dual Yang-Mills Systems with Supergauge Groups
J. LaChapelle, M. Legare
Super-matrix KdV and super-generalized non-linear Schrodinger equations are shown to arise from a symmetry reduction of ordinary self-dual Yang-Mills equations with supergauge grou…
Symmetry Reductions of the Lax Pair of the Four-Dimensional Euclidean Self-Dual Yang-Mills Equations
M. Legare
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…