Narrow Results

We study a system of equations modeling the stationary motion of incompressible electrical conducting fluid. Based on methods of Clifford analysis, we rewrite the system of magnetohydrodynamics fluid in the hypercomplex formulation and represent its solution in Clifford operator terms.

Standard (Arnold–Liouville) integrable systems are intimately related to complex rotations. One can define a generalization of these, sharing many of their properties, where complex rotations are replaced by quaternionic ones, and more generally by the action of a Clifford group. Such a generalization is not limited to integrable systems but — in the quaternionic case — goes over to a generalization of standard Hamilton dynamics.